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Optimization of the ion extraction from an inductively coupled plasma (ICP) by IBSimu modeling. Questo lavoro di tesi nalizzato a raggiungere una pi profonda comprensione del processo di estrazione di un fascio di ioni da un Inductively Coupled Plasma accoppiato a uno spettrometro di massa (utilizzato per l'analisi di soluzioni radioattive). In particolare, lo studio stato focalizzato sulla plasma torch e sull'extraction interface - costituita da sampler e skimmer. Per capire i processi che avvengono tra lo skimmer - a valle del quale il plasma perde la sua quasi-neutralit - e la prima lente ottica, stato utilizzato IBSimu, un software appositamente creato per simulare l'estrazione di ioni ed elettroni da una sorgente di plasma. As said in the previous section, nowadays one of the most important meth- ods in atomic spectrometry is the ICP-MS: the two main reasons for its success are the true multi-element capabilities and the extremely low detec- tion limits. All ICP sector eld instruments consist of [41]: ' an Essay on Fluoride Ion-Selective, ion source (see chapter 3 for a detailed description); ' a sampling interface (see chapter 4 for a detailed description); ' an electrostatic lens system, used to guide, focus and and Using Teams accelerate the positively charged ion beam onto the entrance slit and to shape the beam, giving it a more rectangular prole (in accordance to the ge- ometry of the entrance slit); ' a magnetic sector, which bends ions according to their momentum; the Essay Ion-Selective electromagnet is typically operating in Alzheimer’s Essay examples static mode (that is, at a constant eld) and the eld strength can be changed varying the Essay electric current; ' an electric sector, where dierences in ion energies are compensated to a certain extent; ' a curved ight tube, between the music poles of the Essay on Fluoride Ion-Selective electromagnet; ' an entrance and an exit slit, to shape the geometry of the ion beam and to achieve a good resolution (which depends on the width of the incident ion beam and thus on the width of the entrance slit) ; ' zoom and/or lter optics: in the Neptune, a zoom lens and an en- ergy lter, in order to maintain the direct guidance of the incoming ion beams into the detector and to permit ions with suciently high kinetic energies to pass only; ' a detection system, consisting - in the Neptune - of a number of Fara- day detectors, arranged along the focal plane to measure all isotopes of interest simultaneously; in addition, there are also electron mul- tipliers, discrete dynode detectors and channeltrons to monitor low isotopic abundance nuclides; ' a vacuum system, otherwise the ions would scatter and there would be a signicant loss of transmission and sensitivity (see later for more details about psycho dierent pressure regions). It has to be underlined that two dierent congurations are possible; in the studied case the plasma source and the extraction interface are grounded, as ions are accelerated by the lens system potential. Other instruments have the opposite conguration, with the ion acceleration provided by the 8 Figure 2.5: Schematic drawing of the Neptune MC-ICP-MS (Thermo Sci- entic) [41]. Essay On Fluoride Electrodes! interface, posed at a high voltage. The disadvantage of this solution is that all mechanical parts have to be isolated. Moreover the risk of discharges caused by of politics the conducting plasma is high [24].

The number of articles re- porting this alternative arrangement is low [16] [17] [24]. With both this settlement is possible to do High Resolution Mass Spectrometry (HR-MS). Essay On Fluoride Ion-Selective Electrodes! The present work is focused on Building Good Workplace the mass spectrometry rst step: the analyte ionization through an ICP; therefore the following argumentation will be focused on the plasma source.9 2.3 ICP-MS applications. In order to complete the ICP-MS introduction, an overview on Essay on Fluoride the possible applications is shower provided in the following. Referring to on Fluoride Ion-Selective, the examples chosen by Jakubowski et al. [42] in the sector eld devices area, it is lasswell's definition of politics possible to Electrodes, group the applications in three categories: ' multi-element analysis, ' isotope ratio applications, 9Nowadays, ICP sources have a similar design in mccandless all commercially available instru- ments, independently on the type of Essay on Fluoride Ion-Selective, mass separator [41].

9 Figure 2.6: Schematic of an ICP-MS system. Psycho Music! Various gaseous (dashed lines) and liquid (solid lines) sample introduction devices are shown [46]. Essay On Fluoride Ion-Selective Electrodes! ' speciation analysis. Multi-element analysis has been the lasswell's of politics major application area of sector eld (SF) instruments during the last 15 years. The main reasons for their success are the capability of multi-element measurements, high sensitivity, low detection limits and fast and Essay on Fluoride Ion-Selective accurate direct data acquisition of the into the wild majority of nuclides suering from spectral interferences at low mass res- olution. Essay On Fluoride! ICP-SFMS is used for biological and environmental analyses: to psycho music, determine element concentrations in Essay Ion-Selective body uids - such as blood, urine and and Using cerebrospinal uid -, for the detection of trace elements in sections of Essay on Fluoride Ion-Selective Electrodes, hu- man hairs, for monitoring Ca in biological samples - to study Ca pathways and The Importance Essay metabolism -, in water research, to monitor the fate of heavy metals (including Rare Earth Elements) in the environment, for the direct multi- elemental determination of trace elements in diluted sea water and for on Fluoride Electrodes, soil samples analysis - in order to lasswell's definition of politics, monitor heavy metal mobilization. In in- dustrial applications and materials research, ICP-MS is mainly used in on Fluoride Ion-Selective the semi-conductor industry and in the characterization of pure and ultra-pure materials; other applications are quality control of ultra-pure water, am- monia and acids, determination of the Alzheimer’s stoichiometry and trace impurities in thin barium strontium titanate perovskite layers (used in microelectron- ics), assessment of the purity of TlBr single crystals and Essay forensic studies or provenance determination. Essay Examples! Laser Ablation coupled to ICP-SFMS has to Electrodes, be mentioned because it is used either for bulk quantication of elements, for now meaning, depth proling or the identication of contamination spots. Ion-Selective! Concluding, multi-element analysis is used in food and nutrition science - for beverages, 10 vegetables, sh and infant food - and in geological and radionuclide appli- cations - for studying trace element concentrations in chris mccandless the wild geological samples, soils, sea water or sea water particulates10 and radionuclide determination. The superior sensitivity and the capability to avoid spectral interferences by operating at on Fluoride Ion-Selective Electrodes high mass resolution are undeniable advantages for isotopic analysis as well. Applications range in many elds: from biological to en- vironmental samples, from mccandless geological to provenance and migration studies.

Tracer experiments were conducted to investigate elemental uxes in, e.g., the environment or metabolic processes; natural variations in the isotopic composition of selected elements are used for solving problems in a biological context; Pb composition analyses are used to distinguish between natural, geogenic Pb and Ion-Selective anthropogenic Pb; through Sr isotopic analysis11 is pos- sible to trace the provenance of goods, agricultural products, food or even animals and humans - in archaeometry and apocalypse forensics. Even radionuclide applications are important: ICP-SFMS measurements have proven useful in the nuclear industry and in the related environmental and safety aspects. Irradiated nuclear fuel has been analyzed by means of MC-ICP-MS for Essay Ion-Selective Electrodes, the optimization of the apocalypse fuel cycle and for Essay on Fluoride Ion-Selective, safeguard aspects. At last, ICP-MS instruments are used in analytical problems related to biological systems or environment studies; information on speciation is required in order to understand processes related to toxicity, transport and bio-availability of metals or biological processes in which metals are involved. In life science and environmental applications high mass resolution is needed for Teams Workplace Essay, proteins studies (e.g. for the characterization of metal containing or metal-binding proteins in biological systems), analysis and quantication (e.g. for selenoproteins, metalloproteins and protein-bound metals). 10Sea water temperatures can be calculated from Mg/Ca ratios.

11Isotopic and on Fluoride Ion-Selective Electrodes elemental signatures bear the potential of providing unique ngerprints which can be directly related to the origin of the sample investigated. 11 Chapter 3 Plasma torch The ICP is generated in a discharge gas (Argon, in our case) without using any electrode, by the application of a high frequency electrical current to an induction coil, enveloping the plasma torch [41], as it will be explained in the following. The development of ICP sources began in 1942 [5], when Babat published his rst paper on the properties of electrodeless discharges and realized the rst ICP operating at atmospheric pressure. About 20 years later, Reed published two articles on his ingenious approach to The Importance Essay, the stabilization and thermal isolation of the producted plasmas. He under- lined three properties that make ICP a superior source of atomization and Electrodes ionization: high gas temperatures, capability of now meaning, being sustained in noble gas environments and freedom from electrodes (representing a contamina- tion). As a result of on Fluoride Ion-Selective Electrodes, these good analytical performances, studies on ICP were started in 1962 and the rst use of an Inductively Coupled Argon Plasma as an ion source for apocalypse now meaning, mass spectrometry dates from 1978 [12]. Sciex, Inc., introduced the rst commercial instrument for ICP-MS at the 1983 Pittsburgh Conference, which catalyzed an explosive growth of interest in the technique [12]. In fact, until that year, commonly used ion sources were not suitable for the rapid, direct examination of Essay Ion-Selective Electrodes, aqueous samples because extensive sample preparation was required.1 Then, several other instrument companies conducted ICP-MS research and, between 1985 and now meaning 2010, about 20 commercially available instruments were introduced to Essay, the market (con- sidering both the ICP and apocalypse now meaning the GD plasma source) [41]. For a complete list of the commercial sector eld mass spectrometers with plasma based ion sources see Table 3.1.

To understand how an ICP works, it has to be known that high frequency currents owing in an induction coil generate an oscillating magnetic eld, whose lines of force are axially oriented inside the on Fluoride Electrodes coil. In an ICP, the plasma torch - where plasma is generated - is enveloped in 2 or 3 turns of copper tube, cooled with either water or Argon; this settlement produces an electromagnetic inducted eld by a time-varying magnetic eld. The power 1The sample was evaporated onto a lament for thermal ionization or incorporated into an electrode for music, spark ionization before the sample-containing substrate was physi- cally mounted in the vacuum system. Ion-Selective! The associated time requirement for these opera- tions was rendering the Alzheimer’s Disease routine analysis of large numbers of solutions impractical. 12 Table 3.1: Commercial sector eld mass sp ectrometer with plasm a based ion source s 1985-2010 [41] Name Man ufacturer a Y ear of Status T yp e of instrumen t Geometry in tro duction V G 9000 V G Elemen tal 1985 discon tin ued GD-SFMS rev erse Nier-Johnson Plasmatrace I V G Elemen tal 1988 discon tin ued ICP-SFMS Nier-Johnson JMS-Plasmax I JEOL 1991 discon tin ued ICP-SFMS rev erse Nier-Johnson Plasma 54 V G Elemen tal 1992 discon tin ued MC-ICP-SFMS Nier-Johnson Elemen t Finnigan MA T 1993 discon tin ued ICP-SFMS rev erse Nier-Johnson Plasmatrace II V G Elemen tal 1994 discon tin ued ICP-SFMS rev erse Nier-Johnson JMS-Plasmax 2 JEOL 1995 discon tin ued ICP-SFMS rev erse Nier-Johnson Nu Plasma Nu Instrumen ts 1997 discon tin ued MC-ICP-SFMS Nier-Johnson Axiom V G Elemen tal 1998 discon tin ued ICP-SFMS Nier-Johnson Axiom MC V G Elemen tal 1998 discon tin ued MC-ICP-SFMS Nier-Johnson Elemen t 2 Thermo Quest 1998 av ail able ICP-SFMS rev erse Nier-Johnson Nu Plasma 1700 Nu Instrumen ts 1999 av ail able MC-ICP-SFMS Nier-Johnson Neptune Thermo Quest 2000 av ail able MC-ICP-SFMS Nier-Johnson IsoProb e-P GV Instrumen ts 2004 discon tin ued MC-ICP-SFMS magnetic se ctor + hexap ole collision ce ll Elemen t XR Thermo Electron 2004 av ail able ICP-SFMS rev erse Nier-Johnson A ttoM Nu Instrumen ts 2004 av ail able ICP-SFMS Nier-Johnson Elemen t GD Thermo Electron 2005 av ail able GD-SFMS rev erse Nier-Johnson SPECTR O MS Sp ectro Analytical Instrumen ts 2010 av ail able MC-ICP-SFMS Mattauc h-Herzog Nu Plasma II Nu Instrumen ts 2010 av ail able MC-ICP-SFMS Nier-Johnson Astrum Nu Instrumen ts 2010 av ail able GD-SFMS Nier-Johnson Neptune plus Thermo Scien tic 2009 av ail able MC-ICP-SFMS Nier-Johnson a Man ufacturer names are according to their names when the instrumen t w as in tro duced. 13 supply is given by a radio-frequency (rf) generator, that ranges typically between 1 and 1.5 kW, at a frequency of about 27 MHz. A sketch of the plasma torch used by Neptune MC-ICP-MS is represented in Figure 3.1; it is usually referred to as a Fassel torch, from the american chemist Velmer A. Fassel. The following treatise, which aims to give an overall description of the torch, is mainly based on Essay on Fluoride the publications by Fassel [5] and Houk [12], while a detailed nomeclature description of the system can be found elsewhere [7]. To form a stable plasma, a pattern of three Argon ows is needed; so the Fassel torch consists of three concentric quartz or fused silicate glass tubes, carriyng a total Argon ow between 11 and 18 L/min. Since the plasma temperature is so high, a thermal insulation is needed; the outer tube main operation is thus to insulate the psycho shower music device from the outside environment. To this aim, the Reed's vortex stabilization technique is used [5]: a ow of Argon tangentially introduced streams upward, cooling the inside walls of the outermost quartz tube and centering the Ion-Selective Electrodes plasma radially in the tube.

The outer tube has a 2.5 cm diameter and carries a plasma ow between. 10 and 15 L/min; it is Alzheimer’s Essay examples also responsible for the main supply of Ar to on Fluoride Ion-Selective, the plasma. The middle tube provides the auxiliary gas (0.5 '' 2 L/min), whose role is to lift the plasma o the injector. Now Meaning! The auxiliary gas is injected tangentially too, in order to create a vortex and stabilise the plasma. Essay On Fluoride Electrodes! The eect of the previous two tubes is to generate a stable toroidal plasma through the Alzheimer’s Disease centre tube, in which the sample aerosol is Ion-Selective injected. The Argon ionization is started by a spark produced by a Tesla coil; the ions and electrons this way formed interact with the of politics oating magnetic eld given by the load coil. Ion-Selective Electrodes! The result is a high frequency oscillating electron and ion current, which heats the plasma gas to high temperatures: gas-kinetic temperature of 5000 '' 8000 K, ionization temperature of about 7500 K, excitation temperature of 6500''7000 K, and electron temperature of about.

10000 K; then plasma is maintained by inductive heating. The aerosol generated from the sample is either created by nebulization of psycho, a liquid sample solution or consists of solid particles carried by a gas ow when sample material is ablated by a laser; it is then transferred into the centre of the plasma by an Argon gas ow (0.8 '' 1 L/min), through the Essay Ion-Selective Electrodes inner tube. To be eectively atomized and excited, the sample aerosols should remain localized in the interior high-temperature environment of the plasma as long as possible. Mccandless Into The Wild! The sample species employ about 2 ms to reach the observation height of 15 to 20 mm above the load coil (ALC); this time is sucient in an environment with such a temperature (between 5000 K and 8000 K) to give rise to an ecient volatilization and atomization of the sample components and subsequent excitation and Essay on Fluoride Ion-Selective ionization of the atoms thus formed [5].2 The Saha-Eggert equation [1] can be used to estimate the eciency of 2Just for a comparison, the residence times and temperatures experienced by of politics the sample are approximately twice those found in the hottest combustion ames common used in AAS [5]. 14 Figure 3.1: Inductively Coupled Plasma conguration [5]. 15 the ionization for the resulting analyte atoms, using the electron densities and temperatures typical for the ICP discharge: it results that all elements with rst ionization potentials below 8 eV are completely ( 90%) ionized and even elements with rst ionization potentials between 8 and 12 eV are ionized by on Fluoride more than 10% [41]. So the plasma source ionization eciency is much higher for the ICP than for Building and Using, the other devices;3 moreover, referring to atomic spectroscopy, it is also economically convenient.4 Predominantly singly charged ions are generated for Essay on Fluoride Ion-Selective Electrodes, all elements of the periodic table. Thus, the mass spectrum observed mainly consists of signals corresponding to the singly charged elemental ions of the nuclides of all elements present in the sample. Lasswell's! ICP sources had been developed for optical spectroscopy; when they were adapted for mass spectrometry, secondary discharges (called pinches or pinch eects) between the plasma and the sampler arose. They were caused by the rf potential in the plasma and they gave rise to numerous deleterious eects: rapid deterioration of the Essay on Fluoride Ion-Selective sampling and the skimming cones, contamination of the plasma with sampler and skimmer material, high photon noise and high ion energies with large energy spreads [31]. In order to decrease this phenomenon, the Neptune torch is equipped with a guard electrode (GE), also called torch shield or capacity decoupling.

This is a grounded platinum foil placed in between the plasma torch and the load coil. Since one end of the coil is connected to the rf source and into the wild the other end is grounded, a potential gradient exists along the coil, which becomes capacitively coupled into the plasma. Essay Ion-Selective! The plasma, in turn, is electrically coupled through the sheath (see chapter 4) to lasswell's, the sampler. These two impedance sources act as a potential divider; if plasma potential is too high a strong secondary discharge forms between the plasma and the sampling orice [29]. Gray showed [11] that insertion of a grounded, slotted metal cylinder (the torch shield shown in Figure 3.2) between the load coil and the outer wall of the torch shields the d.c. Essay Electrodes! potential component from the plasma and provides a low plasma potential - in the following it will be shown that this last gain improves the operation of the ICP-MS. Of Politics! In addition, the guard electrode decreases the ion energy spread, and thus can help to increase the overall ion transmission [41]. In order to Electrodes, minimize the plasma potential and secondary discharge, mainly two other dierent load coil congurations have been used:5 ' inverted (or reversed) load coil: the load coil is Essay grounded at the down- stream end nearest the sampler; ' center-tapped load coil: a high voltage of equal amplitude but opposite phase is applied to the coil edges, while the center is connected to ground. Essay! 3In the mccandless Thermal Ionization Mass Spectrometry is lower than 5%. 4The operating cost of these plasmas owing in the Fassel torch, exclusive of the electrical power, is on Fluoride lower than the cost of the gases needed to operate the nitrous oxide- acetylene ame commonly used in Atomic Absorption Spectroscpy (AAS).

5Also the and Using Good Teams in the Workplace interleaved and the balanced load coils have been studied [31]. 16 Figure 3.2: Sketch of Essay Ion-Selective Electrodes, a plasma torch in which is clearly visible the guard electrode. Figure 3.3: Design features of an inverted load-coil (A) and a center-tapped coil (B) [20]. 17 Chapter 4 Extraction interface In coupling an Inductively Coupled Plasma and examples a Mass Spectrometer, the trouble is that ICP operates at atmospheric pressure, whereas MS requires an ultra high vacuum (UHV) condition (operating pressure less then 10''7 Pa), otherwise the ions would be scattered by the gas atoms. The solution to such a pressure discrepancy is to interpose three interfaces between the gas source and the analyzer, resulting in a four-regions solution. While the rst one is at ambient pressure (105 Pa), the second region (called interface) is pumped by on Fluoride Ion-Selective Electrodes a regular rotary pump, to obtain a pressure of lasswell's definition of politics, 2 102 Pa.

The higher is the grade of vacuum, the better are the instrumental performances features, such as transmission eciency or abundance sensitivity; as a con- sequence, stronger vacuum pumps are becoming popular. On Fluoride! To preserve the high vacuum condition in the third region, a slide valve is interposed; it is only opened when the plasma is operating stable and is closed before plasma shutdown, to isolate the high vacuum. The third region, where lenses are located, has a pressure of about 5 10''2 Pa, while the mass spectrometer (nal region) operates in ultra high vacuum conditions (about 10''7 Pa). It has been found that such a low pressure is definition advantageous in the case of multi collector devices [41]; in order to provide this result, the analyzer is Essay Ion-Selective separated from the lens system by a second valve and additional ion getter pumps are required. The development and improvement of the ion sampling interface for psycho, ICP-MS have been crucial aspects of the success of the technique. The rst analytical mass spectrometer for ion sampling from an ICP used a stagnant layer type sampling interface [6] [10]1. At the end of the plasma torch, an interface was present to extract a small fraction of plasma with its ions into a vacuum system.

This interface was composed by two cones, a sampler and Ion-Selective a skimmer. The rst one consisted of a water-cooled copper cone, on whose tip was mounted a molybdenum disk, through whose center was drilled a 50 m diameter orice. The Importance Essay! Due to Ion-Selective, this small diameter, an aero- dynamically stagnant layer of gas formed between the two cones, as shown in Figure 4.1. 1This type of pinhole sampler was adopted in apocalypse now meaning the early days from on Fluoride Electrodes ame and plasma sampling methodology and from the original work of Gray with a d.c. capillary arc plasma [6]. 18 Figure 4.1: Diagram of boundary layer sampling interface for ICP-MS [10]. Since electrons are faster than ions, a space-charge sheath containing an excess of ions builded up around the tip of the cone. This stagnant bound- ary layer was in thermal contact with the relatively cool sampler, making the mccandless layer temperature intermediate between the on Fluoride Ion-Selective plasma one and of Integrity Essay the sam- pler one. As the boundary layer was extended across the sampler tip, ions were extracted only after a large number (about 106) of collisions with the layer. This transport through the boundary layer induced several liabilities: rst of all it was probably facilitating ion-electron recombination, ion neu- tralization at the sampler walls, charge exchange, ion-neutral attachment, nucleation and condensation of solid deposits (mainly due to Essay Ion-Selective Electrodes, the formation of involatile metal compounds) and some occurring reactions might have been catalyzed by the metal surface of the orice disk. Secondly, consid- ering the supersonic jet downstream the apocalypse sampler cone, collisions leading to clustering, ion-electron recombination or charge exchange also occurred. Essay Ion-Selective Electrodes! Consequently, sample deposition occurred in the sampling orice - metal oxide and metal hydroxide ions had been observed.

Progressive solid con- densation of sample material both made the extraction eciency of analyte ions gradual decreasing and chris the wild restricted the on Fluoride Electrodes useful life of orices. Even nowa- days the rst components that have to be changed in a mass spectrometer are the sampler and the skimmer cones: their lifetime is limited by psycho music the sputtering in on Fluoride Ion-Selective the region immediately behind the aperture [8]. Back to the problem of solid deposition, with this conguration biological uids required a dilution factor of several hundred before analyses of such solutions could be performed for more than one hour. The consequent deterioration in apocalypse powers of detection for analyte elements was not acceptable for various ap- plications. Owing to the diculties arised with this type of sampling, a new 19 sampling interface has been adopted: the supersonic nozzle and skimmer [10].2 The version of this technique used in Essay Electrodes our ICP-MS consists of a large sampling orice: with this conguration it is lasswell's of politics possible to Electrodes, break through the chris the wild intermediate sheath and to have a continuum gas ow condition. The sheath is a thin ply around the inner edge of the sampling orice; in this ply the charged particles shield the rest of the gas ow from the potential on the sampler (usually grounded). Therefore the extracted ow passes through the sampler as a quasineutral plasma,3 i.e. On Fluoride! with essentially equal densities of mccandless the wild, ions and Essay on Fluoride electrons.4 Cool layers are still present, but they form obliquely around the inside edge of the orice, instead of across its mouth [29]. Consequently the Building and Using Workplace Essay salt deposition and Essay on Fluoride Electrodes the oxide ion formation are much less severe [10]. And Using Teams In The Essay! So, this conguration provides several advantages: ' a much higher total ow of ions; ' a more representative sample of ions from the plasma; ' greater resistance to plugging from Essay deposited solids.

The improved resistance to erosion and expansion is also because such an orice is made with relatively thick metal near the tip. Apocalypse Now Meaning! Figure 4.2 is a scale drawing of continuum sampling interface. The sampler (or nozzle) (A) is a nickel-made cone, in which tip is drilled a 0.8 mm diameter orice with a length of 0.25 mm. The internal and external sampler angles are 90' and 120', respectively. Coaxially placed, 7 mm downstream the sampler, there is the skimmer, made from stainless steel with 50' and 60' internal and external angles, respectively.5 The short distance between the two cones allows a sequential pressure decrease and it could be varied by Essay on Fluoride changing the thickness of the Teon spacer (C). Both the sampler and skimmer are grounded; nevertheless there could be some benets applying a voltage to the skimmer - see section 7. From the work by Hu et al. Lasswell's Definition Of Politics! [22] it results that larger sampling orices could bring higher ion signals: the Essay Ion-Selective plot in apocalypse Figure 4.3 shows how the Co and Bi ion count rate increased drilling out the circular aperture progres- sively. Since also the Essay Ion-Selective Electrodes background pressure increased after each drilling, it was necessary to empirically adjust the chris mccandless into the wild separation between the sampler and Essay on Fluoride Ion-Selective the skimmer to maximize the ion signal. Moreover, a small orice is more subjected to clogging compared to psycho shower, a bigger one: as it can be seen in Figure 4.4 a pressure decreasing in the case of the smaller orice is Essay Ion-Selective Electrodes observed, since it plugs quickly. In conclusion, enlarging the orice could provide a double 2This type of sampling interface have been in use since the pioneering work of psycho music, Kantrowitz and Grey in on Fluoride Ion-Selective Electrodes 1951 [2]. 3The charge density is apocalypse considered to be suciently high as to ensure that the charac- teristic Debye length is Essay small with respect to the dimensions of the interface components - under this condition it's possible to consider the beam as neutral.

4This concept is supported by calculations based on a paper by Axford and Hayhurst. Apocalypse! 5Nowadays, dierent skimmer cone designs are available, characterized by dierent transmission eciency [44]. 20 Figure 4.2: Scale drawing of continuum sampling interface for ICP-MS [10]. Essay On Fluoride Ion-Selective Electrodes! 21 Figure 4.3: Ion count rates as a function of sampler orice diameter [22]. benet: a higher ion signal and an improved tolerance to orice plugging. However it has to be underlined that these studies were conducted with a continuous ow ultrasonic nebulizer, which transported material to the plasma at Alzheimer’s a rate at least 10 times greater than the one obtained with a con- ventional pneumatic nebulizer. As a consequence, the second improvement would not be relevant in our case. On Fluoride Ion-Selective Electrodes! In order to understand the performance of this interface and particu- larly to now meaning, nd the Electrodes parameters needed in The Importance of Integrity Essay the simulations (see section 6.4) the gas ow (in molecules/s) through the sampler can be calculated through equation (4.1) [9] used by Olivares and Houk in their article (dating 1985): U0 = 'f ()NAD 2 0 P0 4 '' mRT0 (4.1) where f() = '' [2/( + 1)](+1)/2(''1) , NA is Avogadro's number, D0 the orice diameter, P0 the ICP pressure, m the mean molecular weight of Argon, R the gas constant, T0 the source gas temperature of the ICP, and is the specic heat ratio at constant pressure and Essay on Fluoride Ion-Selective Electrodes volume (Cp/Cv) of Argon. 22 Figure 4.4: Normalized interface pressure as a function of time for continu- ous nebulization of 1000 ppm Y at sampling orice [22]. 23 The ow through the skimmer cone is given by the following equation: US = U0 f () DS XS 2 (4.2) where DS is the skimmer diameter and XS the skimmer-to-sampler distance. These theoretical results are in Building in the good agreement with the experimentally obtained values for an ICP with 10 mg/l Co solution [10].

In a 1988 article, Douglas and French provided another way to describe the gas expansion through these two orices; in their article the gas ow across the sampler was given by [47] G0 = 0.445 n0 a0 D 2 0 (4.3) where n0 is the source number density and a0 the speed of sound in Electrodes the source: a0 = k T0 m (4.4) (k is the Boltzmann's constant). The equation for the gas ow through the lasswell's skimmer uses the Essay Electrodes gas density and the ow velocity at the skimmer tip, n(xS) and Disease v(xS) respectively, and the area of the skimmer orice AS:6 GS = n(xS) v(xS) AS (4.5) These two models (the one by Olivares and Houk and the one by Douglas and French) are based on Essay on Fluoride a common assumption: as the plasma plume is expanding from a sonic orice into a region of lower pressure, it produces the shower music development of the free jet shock wave system [4]. Essay Ion-Selective! As it can be seen in the cross sectional view showed in Figure 4.5, the ow eld consists of a dark core portion, named zone of silence (unaected by the pressure changes along the jet boundary), laterally bounded from mccandless into a barrel shock and ending with the so called Mach disk (its thickness has been found to be of the order of magnitude of the Essay Ion-Selective mean free path [34]). Psycho Shower Music! This phenomenon has been well characterised by Ashkenas and Essay on Fluoride Electrodes Sherman [3]; they calculated the distance downstream the sampler at which the Mach disk forms: xM = 0.67D0 p P0/P1 (4.6) where P1 is the chris into interface background pressure. This relationship has been conrmed experimentally by optical measurements of Essay on Fluoride Ion-Selective Electrodes, emission excited in the Mach disk [29]. As the gas passes through the sampler, it expands adiabatically into the low pressure region; since the mean free path () is Good much smaller than the diameter orice, several collisions between fast atoms from the dark core and background atoms occur. This phenomenon causes the on Fluoride Ion-Selective Electrodes formation of the Mach disk and the barrel shock, depicted in Figure 4.5. Mccandless Into! Moreover, through 6The ow velocity is Essay on Fluoride Electrodes nearly constant at Teams in the p5kT 0/2m . 24 Figure 4.5: Cross sectional view of supersonic expansion behind the sampler [29]. this scattering process, the random thermal motion of atoms in the plasma is converted into directed motion in the zone of silence: the ow velocity can than exceed the local speed of sound and the Mach number becomes greater than one (M 1).7 The Mach disk formation is observable analyzing atom velocities and temperatures (showed in Figures 4.6 and 4.7) as a function of distance downstream the sampler cone. The rapid acceleration and cooling of the atoms are expected from a supersonic expansion [34] and is represented by the series of point that start about on Fluoride 2 mm downstream the sampler. Alzheimer’s Disease Examples! At a position of about 10 mm another population of atoms forms: this new population, slow and on Fluoride Ion-Selective hot, is given by fast atoms which collide with background atoms and constitutes the Mach disk.

In order to nd a numerical result for the gas ow through both the sampler and the skimmer using the two models previously shown, some other relations are needed. Into The Wild! The Mach number in the plasma is less than one (M 1); as the gas passes through the sampler the Essay density decreases, the ow speed increases and M increases too. In this region the apocalypse now meaning centerline Mach number for a monoatomic gas - as in Electrodes this case - is given to a very good approximation by M = 3.26(x/D0) 2/3 '' 0.61(x/D 0) ''2/3 (4.7) where x is the axial distance behind the orice. This means the Mach number reaches 1 at a distance equal to Workplace, 0.5 orice diameters downstream 7The Mach number is dened as the on Fluoride ratio between between the gas ow speed (u) and the local speed of sound (a0). 25 Figure 4.6: Axial velocity dependence downstream from the sampler cone: 4 fast, cold component, slow, hot component [34]. Figure 4.7: Axial temperature dependence downstream from the sampler cone: 4 fast, cold component, slow, hot component [34]. 26 Figure 4.8: Scatter plot of the gas temperature as a function of the distance from the sampler in the free jet, obtained from equation (4.9). the Alzheimer’s Essay examples sampler. Furthermore the gas density and temperature decrease inside the jet, according to the following equations: n0 n = 1 + M 2 '' 1 2 1/(''1) (4.8) T0 T = 1 + M 2 '' 1 2 (4.9) where n0 and T0 are the gas density and temperature in the source.

Equation (4.8) could be approximated back to the onset of the Mach disk by on Fluoride Ion-Selective Electrodes n(x) = 0.161 n0 (D0/x) 2 (4.10) This relation, that describes the drop in intensity of neutral species along the centerline, has been experimentally conrmed by Alzheimer’s Essay examples Niu and Houk, when in 1994 they measured electron densities in the interface with a Langmuir probe [27]. The plot in Figure 4.8 represents the temperature drop described by equation (4.9); this decrease corresponds to a narrowing of the width of the velocity distribution (Figure 4.9) as the random thermal motion is converted into directed motion with a relatively uniform speed. A combination of all the displayed equations have been used to Essay, obtained the chris mccandless the wild results highlighted in Table 4.1. The gas ows have been obtained with two dierent equations and are in good agreement, especially in correspondence of the sampler cone. In 27 Table. 4.1: Parameters and. constan ts used to calculate the. o w - highligh ted.

skimmer with tw o dieren t mo. Houk [10] Douglas and. h [14] 1 .67 sp ecic heat ratio C p /C v 1 .67 sp ecic heat ratio C p /C v f ( ) 0 .726661 T 0 5000 K gas. temp eratur e D sa 0 .8. mm sampler diamete r m 6 .6 10 23 g relativ e atomic mass P 0 10 5 Pa ICP pressure D sa 0 .8. mm sampler diameter M 39. g/mol relativ e molecular w eigh. t a 0 1317 .97 m/s sp eed. of sound in the. source T 0 5000 K gas. temp erature n 0 1 .5 10 18 cm '' 3 source densit y x 7. mm sampler to skimmer distance U 0 5 .4 10 20 atoms/s gas.

o w through the. sampler G 0 5 .6 10 20 atoms/s gas. o w through the. sampler D sk 0 .8. mm skimmer diame ter M sk 14 Mac. mm sampler to skimmer distance n sk 3 .0 10 15 cm '' 3 gas. densit y at the. skimmer P i 861 Pa impact pressure at the. skimmer v 1 .6 10 5 cm/s o w velo cit y D sk 0 .8. mm skimmer diameter U S 5 .1 10 18 atoms/s gas.

o w through the. skimmer G S 2 .5 10 18 atoms/s gas. o w through the. skimmer 28 Figure 4.9: Wide velocity distribution in the plasma compared to the nar- rower distribution in the supersonic jet [29]. the Essay Electrodes region close to the skimmer there is a factor 2 between the Good in the Workplace two models results; this dierence is negligible since the gas ow probably depends on many other contributions - e.g. the analyte species, the nebulizer gas ow - that can signicantly aect the nal result. Regarding the sampler to Essay Ion-Selective Electrodes, skimmer distance, Douglas and French showed that the best arrangement corresponds to having the skimmer tip about. 2/3 of the way back to the onset of the Mach disk [14] [29]. This result approximately agrees with the apocalypse one obtained for the maximum intensity in the case of a neutral beam from Campargue expansion [29]: XS = 0.125 D0 D0P0 P1 1/3 (4.11) Even if here is referred to as the mean free path inside the sampler orice, it has no particular subscript as it is expected to be nearly equal to the one for the gas outside the sampler in the ICP.

The skimmer protrudes into the zone of silence so that shock waves form behind the skimmer tip o the outside walls of the on Fluoride skimmer, as shown in the sketch in Figure 4.10. The Importance! With this conguration, the metal wall of the skimmer where the second shock wave begins is thick enough to Ion-Selective, conduct away the heat generated and the thin edge of metal at the skimmer tip remains stable. Otherwise, if the skimmer was located after the Mach disk, the sampled gas would be reheated by collisions with background gas in the Mach disk; this process would lead to the formation of a spherical white emitting region. The heat this way producted would be directly transferred to the skimmer tip, too thin to properly conduct the heat away; the result would be the melting or the Building and Using Good Teams in the Workplace Essay rapid degradation of the skimmer tip [29]. Calculation of the Knudsen number Kn, especially at the skimmer, is also instructive; it is dened as the ratio of the on Fluoride Electrodes mean free path to lasswell's definition, the 29 Figure 4.10: Eect of dierent sampler-skimmer distances. On Fluoride! (a) Skimmer at normal position used for analysis. Disease! (b) Skimmer outside the zone of silence [29].

30 skimmer diameter DS: Kn = DS (4.12) In the Essay on Fluoride small scale Kn quanties the failure of the definition of politics Navier-Stokes description: in fact this model corresponds to the collision-dominated transport limit of on Fluoride, small Knudsen number Kn 1. Teams! More specically, in the presence of hy- drodynamic gradients in a homogeneous gas over lenghtscales characterized by Kn 1, the Essay Ion-Selective Chapman-Enskog expansion procedure can be applied to the governing kinetic (Boltzmann) equation to now meaning, show that the gas response can be described by linear-gradient constitutive relations which lead to the Navier-Stokes description [33]. Practically, the lower the Kn, the smaller the number of collisions is; Kn would have to be much less than unity (i.e. DS ) for the beam to expand through the skimmer without collisions. The mean free path can be expressed through the Essay Ion-Selective Electrodes following relation, based on chris mccandless the wild viscosity measurements and kinetic theory arguments [47]: = 16/5 nm q 2'kT m = 16/5 n '' 2'kT m (4.13) where n is the molecular number density, m the Essay on Fluoride Ion-Selective Electrodes particle mass and k the Boltzmann's constant. It is possible to refer to the viscosity coecient both with and . Niu and Houk report another relation for the Knudsen number: Kn = DS = 1 1.414''nDS (4.14) where ' is the Alzheimer’s Disease Essay examples gas kinetic cross section for Ar (4.1 10''15 cm2). The result obtained applying these two relations with the settings previously described are Kn = 0.3 and = 0.2. These values are consistent with several articles [10] [14] [26] [29]. Essay On Fluoride! The literature concerning supersonic expansions indicates that in this case two main disturbances are to be expected around the tip [26]: a thin shock in front of the chris mccandless into skimmer and perturbation of the straight line beam ow by on Fluoride Electrodes collisions of the beam with atoms reected from the skimmer wall. Considering now the gas ow rate calculated for Essay, our particular case, the- oretically the Essay Ion-Selective total ion current at of Integrity Essay the base of the skimmer should be about.

0.4 mA; this result is consistent with several papers: for example, Gillson et al. [15], even if with a slightly dierent setting, calculated an ion current of. 1016 ions/second, corresponding to Essay, 1.5 mA. This current has been calculated considering that through the skimmer passes only 2.6% of the central ow of the lasswell's ICP. Considering the theoretical loss of analyte ions for Y, Chen and Houk calculated a transmission eciency from the skimmer to the detector is 0.02%. As a consequence, the overall eciency of an Essay on Fluoride Electrodes, ICP-MS is about. 510''6 ; in other words, theoretically, for every 106 analyte ions in definition of politics the central channel of the ICP, only ve ions reach the detector. As it will be explained later, this number is even lower in the reality. Through a comparison with a three-aperture ICP-MS interface, they deduced that many ions are lost between the skimmer tip and Essay on Fluoride the ion optics or inside the ion optics itself. So 31 it is crucial to understand what happens in this region and Alzheimer’s how ions are lost. Chapter 6 is Essay on Fluoride aimed to simulate the region where particles y, including the skimmer and the rst lens (named extraction lens), in order to Alzheimer’s Essay examples, study and on Fluoride Ion-Selective characterize the apocalypse formed beam.

Resuming the work by Gillson et al., they repeated the ion current measurements8 with the same settings for a heavier ion (U+); the ux resulted higher. This phenomenon is called instrumental mass discrimination and Essay on Fluoride Electrodes has been deeply investigated (e.g., by Kivel et al. Chris Into The Wild! [43]), since it hampers accurate determination of absolute isotope ratios. Ion-Selective! In general, it consists in having at the spectrometer a stoichiometric composi- tion dierent from the now meaning one characterizing the original sample material. It has been reported that, typically, analyzing two isotopes, the heavier has a higher transport eciency: the dierence is about 10 '' 20% in the case of light elements and down to Essay Ion-Selective Electrodes, 1% for heavy elements. Four main factors are at the base of chris the wild, mass discrimination: ' sample introduction and ion generation; ' collisions; ' space charge eect; ' energy-selective ion transmission. The rst and the last one are not studied in the present work, since it is limited to the region dened by the skimmer and on Fluoride Electrodes the rst ion lens. The Importance! As the plasma is quasi-neutral until the starting of the skimmer, it's reason- able to assume that mass discrimination in Essay on Fluoride the interface is mainly caused by collisions.

This hypothesis is consistent with the work by Taylor and Farnsworth [44]: they found the absence of any space charge eect dur- ing the ion transfer from the source to the spectrometer. Moreover, for the present work, collisions have been considered a negligible contribution compared to space charge eect. As a consequence, mass discrimination upstream the skimmer has not been considered; the apocalypse following investigation is limited to the region downstream the skimmer cone, up to the extraction lens.9 Resuming mass discrimination due to space charge eects, it can be explained by postulating that the Ion-Selective Electrodes ion beam within the Good Teams in the skimmer is space charge limited: its density is so high that mutual repulsion will not allow the ions to Essay Electrodes, remain tightly focused. Since all ions have the same charge, they are subjected to the same force: as a consequence, lighter ions are de- focused (and then colliding on the skimmer walls) much more readily than heavier ones. Definition! More than upstream, the space charge is considerable in the region downstream the skimmer. In fact, according to Electrodes, the model by Douglas and French [14], plasma is sampled without signicant charge separation.10 8They used a stainless steel collector - situated 1 in. The Importance Essay! from the base at the skimmer - consisting of three concentric rings and a central circular stop.

9Study of mass discrimination after charge separation can be found elsewhere [43]. 10In an alternate model, presented by Chambers et al., it is assumed that signicant charge separation occurs between the Ion-Selective sampler and the skimmer; therefore the ion current through the skimmer would be signicantly less than that estimated in The Importance this work. 32 Behind the skimmer, where the beam expands, there are three main con- tributions to the loss of the ions: the density decreasing - proportionally to 1/x2 (where x is the distance from the skimmer) - as a consequence of the expansion, the beam spreading and the preferential loss of Essay, electrons. This last phenomenon could be explained considering the Debye length D; downstream of the skimmer D is signicant compared to the dimensions of the beam and electrons are lost readily to The Importance of Integrity Essay, the inner wall of the skimmer because their high mobility. Moreover, in this stage, the electrostatic eld penetration from the extraction lens becomes signicant; as a consequence of these two eects, electrons leave a net axial positive space charge [21]. Its signicance can be quantitatively described using the perveance P [28]: P = I V 3/2 (4.15) where I is the total current and V the accelerating potential. P depends only on the geometry of the extractor and on Ion-Selective the type of the particle [28]. For a singly charged ion beam, space charge is negligible if P 10 ''8 (m ion/me) ''1/2 (4.16) where mion and me are, respectively, the mass of the particle and apocalypse of the Essay on Fluoride Ion-Selective Electrodes electron. So, for Argon ions, the maximum perveance without signicant space charge eects is definition 3.710''11. In the proximity of the skimmer P is equal to 1.9 10''7 [28], which exceeds the on Fluoride Ion-Selective maximum perveance by more than a factor 5000. To obtain a rough estimate for the maximum electron current (for argon), it is possible to assume the skimmer as a cylinder with diameter.

D and of Integrity length L:11 Ie,max(A) = 38.6 10 ''6V 3/2 D L 2 (4.17) The ion current is Electrodes related to shower music, the electron one: Iion Ie = r me mion (4.18) therefore Iion,max(A) = 9.04 10 ''7 r z mion V 3/2 D L 2 (4.19) As hinted before, another cause of on Fluoride, losing ions is the rarefaction of the beam as it travels farther from the skimmer tip. The Debye length in- creasing, by chris mccandless into virtue of its inverse square root dependence on the ion density, causes also the ions (not only the electrons) spreading. So, to enhance the transmission eciency, the Essay on Fluoride Ion-Selective Electrodes distance between the skimmer tip and the ion optics has to of Integrity Essay, be minimized. A substantial increase in ion signal was 11The diameter at Essay the base of the skimmer is equal to its length; the average diameter of the skimmer is then about L/2 and and Using Workplace Essay the ratio D/L is about 0.5. 33 seen when this separation was reduced to 2.4 cm [22]. At this position, the mouth of the rst lens was only Ion-Selective Electrodes 5 mm from the apocalypse nearest surface of the skimmer wall. Closer separations were tried, but the Essay on Fluoride Ion-Selective voltage output for the rst lens became unstable, because of an electrical discharge between the and Using ion lens and the skimmer wall or due to a high current ow to the lens. On Fluoride! In the Neptune MC-ICP-MS is the now meaning thickness of the separation valve limits the smaller distance between the skimmer and Essay on Fluoride Ion-Selective Electrodes the lens.

Table 4.2: Resume of the torch and the extraction interface operating pa- rameters Forward power 1350 W Guard electrode Grounded Gas ows: Cool 14.6 L/min Auxiliary 0.9 L/min Sample 0.8 L/min Make-up 0.3 '' 0.5 L/min Injector Sapphire (narrow bore) Spray chamber APEX HF Cones:12 Sampler Aluminium 0.9 mm Skimmer Aluminium 1.0 mm 12Custom design by PSI. 34 Chapter 5 IBSimu To simulate what happens during the beam extraction from the plasma source, an ion optical computer simulation package have been used, IBSimu. Alzheimer’s! This software is designed especially for the ion source community [40] and it is well suited for our particular aim because it is conceived for ion (both positive and negative) and electron plasma extraction. Its development started at LBNL in 2004 where it was used to Ion-Selective Electrodes, design a slit-beam plasma extraction and Good Teams in the Essay nanosecond scale chopping for pulsed neutron generator. Later, at the University of Electrodes, Jyvskyl (Finland), Department of Physics (JYFL), the code was made modular and suitable for many dierent types of problems. IBSimu has been documented and psycho shower released with an open source license (it can be downloaded at: http://ibsimu.sourceforge.net/) and so it's well suited for use in the scientic community. It is used as a computer library through a C++ interface and it presents several peculiar advantages: ' power and Essay Electrodes versatility; ' customization and inclusion of new modules; ' automation and batch processing; ' incorporation of code in other software; ' easiness of use (on the psycho main site there are two tutorials http:// ibsimu.sourceforge.net/tutorial.html and the reference manual http://ibsimu.sourceforge.net/manual_1_0_5new_solver/index. html); ' possibility to do the diagnostics from code or with an interactive tool; ' data exporting and visualization. The code is Essay on Fluoride capable of solving electric elds in 1D, 2D (planar or cylin- drical symmetry) or full 3D simulation geometries and it can calculate rel- ativistic continuous wave or pulsed particle trajectories taking into account the space charge density. The starting point is the denition of the ge- ometry, where the apocalypse now meaning simulation is done, and the electrodes (including the Essay Electrodes 35 Figure 5.1: Operational diagram for solving the Poisson problem[40]. grounded interfaces), using a mathematical description. In order to calcu- late the electric potential, the simulation domain is divided in apocalypse square meshes with constant step size, which dimension can be specied in the geometry section of the Electrodes code. So the eld where particles y is discretized: for each cell the Disease Poisson's equation '' 2' = '' 0 (5.1) is solved using nite dierence method (FDM) on the nodes of the mesh.

Then, the Ion-Selective Electrodes electrostatic potential is calculated through a solver, using an iterative approach (described in the following). Disease Essay! The nite dierence representation for a vacuum node i is: 'i''1 '' 2'i + 'i+1 h2 = '' i. 0 (5.2) while Neumann (5.3) or Dirichlet (5.4) boundary conditions can be used for boundary nodes. ''3'i + 4'i+1 '' 'i+2 2h = d' dx (5.3) 'i = 'const (5.4) To achieve smooth electric elds on the solid edges, the edge nodes within the solids are adjusted to on Fluoride, virtual potentials using subnode information about the geometry: '(x0 '' h) '' ( + )'(x0) + '(x0 + h) 1. 2 ( + )h 2 = '' (x0) 0 (5.5) On the edges of the simulation domain, every solver supports Dirich- let and Neumann (rst and second order approximations) boundary condi- tions. The calculation can also include the generally accepted nonlinear plasma model for positive ion extraction; thermal background electrons of the music plasma are modeled analytically in Poisson's equation (5.1) where. = ion '' e0 exp[(U '' Up)/(kTe/e)] and Essay Ion-Selective the plasma potential Up and the electron temperature Te are the model parameters. Ion charge density ion is calculated from beam current density and electron charge density e0 is set to ion at plasma potential. The electric eld (needed for particle 36 trajectories) is and Using Good in the obtained by numerical dierentiation and interpolation of Essay Electrodes, potential, using nine closest neighboring mesh nodes.

Then, the code cal- culates the particles trajectory integrating the equations of motion, derived from Lorentz force, with adaptive Runge-Kutta Cash-Karp (fourth and fth order) algorithm. In 2D and Alzheimer’s with a null magnetic eld: dx dt = vx dy dt = vy dvx dt = ax = q m Ex dvy dt = ay = q m Ey This method has an automatic step-size adjustment for required trajec- tory accuracy. On Fluoride Ion-Selective! The implementation of the Runge-Kutta algorithm is used from the GNU Scientic Library. As the CPU available was multicore and the particle tracer is multithreaded, for a high eciency calculation eleven cores were used for ying particles and chris the wild one for the potential determination. The particle tracer algorithm nds all the meshes the trajectory passes through and deposits the charge of the Essay particle on the four (eight in 3D) surrounding mesh nodes.

The same procedure checks for collisions in the mesh square. The code in Building Teams Essay Appendix A was the starting point in my work; to under- stand the extraction process and to optimize the fundamental parameters (Up and Te), I changed some parts of Essay on Fluoride Ion-Selective Electrodes, it, as it will be explained in the next chapter. Lasswell's! Hereinafter there is Electrodes a description of the Alzheimer’s examples main operations done by this rst code. After including all libraries needed (most of Essay Ion-Selective, them have been written by Alzheimer’s Essay examples Taneli Kalvas), some denitions are present: the number of iterations, the rst lens acceleration voltage V acc, the plasma potential. Up, the Essay electron temperature of the plasma Te, the number of particles per species n_particles and the kinetic factor Ekin_factor (KF ). The last one is given by the ratio between the kinetic energy KE and the mass m; it is dened in this way in order to be equal for all the particles, regardless of their mass (in fact they are sent with a given velocity, not energy). Building Good Teams In The Workplace! To have the Essay Electrodes kinetic factor in apocalypse eV/amu it has been used the following equation: KF [ eV/amu] = 1.66 10''8 3.2 v 2 (5.6) where v is in m/s. Following the code, a rst array is dened to list the masses of the simulated ions in addition to Argon and another one is for on Fluoride Ion-Selective Electrodes, the beam current (in A). In the section Output denitions it is possible to set (through boolean variables) what to print during the Disease compiling and at the end of the Essay Electrodes 37 code: debug and verbose provide some status information, the GTK plot represents the trend of both the electric potential and space charge error and plotting produces several les (it will be explained in detail later). Before starting the geometry section, the apocalypse now meaning function fname is dened; it is used in Electrodes the plotting phase, to print the name of the dierent les produced in it.

Then, in the geometry section, the skimmer, the interface and of Integrity the ex- traction lens are dened, using a cylindrical simmetry: only the Essay Electrodes upper part is described and then, through a mirror function on x axis, the electric eld in the lower part is obtained. In this section the mesh dimension - really important in Essay the next chapter - is also dened. After the insertion in the geometry of the solid objects, boundary conditions are setted: at on Fluoride the edges of x and y (numbers from 1 to 4) they are of Good Teams in the Essay, Neumann type, while for the user dened electrode (7 and 8) they are of Dirichlet type. At this point the initialization of the plasma and of the solver takes place: since several nonlinear solvers are available, the rst task was to decide which one was more tting our requirements (see section 6.1). The Argon charge density is on Fluoride Ion-Selective calculated and the particles are setted to be mirrored along the x axis. Thus it is possible to chris, start the iteration loop.

This is necessary since there are two contributions to the electric potential: the accelerating voltage (usually. ''2000 V) of the Essay Ion-Selective ion lens and the space charge of the ying particles. As this second factor depends on the particles trajectories, which in turn are determined by the total electric potential, an iterative approach has been adopted. The number of shower, iterations can be set in on Fluoride Electrodes the beginning of the code: const uint n _iter = 21 Then the i index spaces in shower music the range 0 niter in order to reach the convergence. In the following a brief explanation of the operations executed in every cycle is provided: i = 0 : In the rst iteration the electric potential is calculated taking into account the electrodes contribute only, i.e. for = 0. Electrodes! After computing the electric eld, particles are sent. i = 1 : As particles are now present, space charge is calculated and set as a variable in the plasma model; in fact, with IBSimu, plasma is a function of and Using Good Teams in the Essay, space charge , electron temperature Te and plasma potential Up. Then electric potential (and subsequently electric eld) is recalculated, now as a function of Essay on Fluoride Electrodes, both electrodes and ying particles. Alzheimer’s Essay Examples! As the charge density only changes passing from the rst to the second iteration, plasma is calculated only in this step; there is no need to recalculate it in the other steps. For i ' 2: The potential and eld are recalculated and so are the particle trajectories, until both electric potential and space charge converge - i.e. until the Electrodes dierence for psycho, these two parameters between two iteration is nearly zero.

There are dierent function to produce particles, depending on which beam parameters are known: 1. add_2d_beam_with_energy (uint32_t N, double J, double q, double m, double E, double Tp, double Tt, double x1, double y1, double x2, double y2) 38 2. add_2d_beam_with_velocity (uint32_t N, double J, double q, dou- ble m, double v, double dvp, double dvt, double x1, double y1, double x2, double y2) 3. add_2d_KV_beam_with_emittance (uint32_t N, double I, double q, double m, double a, double b, double e, double Ex, double x0, double y0) 4. On Fluoride! add_2d_gaussian_beam_with_emittance (uint32_t N, double I, dou- ble q, double m, double a, double b, double e, double Ex, double x0, double y0) where N is the number of Good in the Workplace Essay, particles, J the beam current density (A/m2), q the charge of beam particle (in multiples of e) and m the mass (u). For the rst two functions, the beam is dened on a line from (x1, y1) to (x2, y2) and it propagates into a direction 90' clockwise from the direction of vector pointing from (x1, y1) to (x2, y2); at the beginning the beam prole is uniform. For the rst function E represents the beam energy (in eV ), while Tp and Tt are the Essay parallel and transverse temperature, respectively, in eV. The particle speeds in lasswell's definition direction i are sampled from a gaussian distribution with standard deviation dvi = p(Ti e/m), where Ti is the beam temper- ature in direction i (eV), e is the electron charge (C) and m is the mass of the ion (kg). With the third function, particles are own in the positive. x -direction from Essay Electrodes a starting location (center point) dened by (x0, y0) and the beam spread in the projectional space is made according to KV/hard- edged (Kapchinsky-Vladimirsky) distribution. I represents the beam total current (in A) and Ex the starting energy of the beam (in eV). The beam is made to match Twiss parameters (a) and Building and Using in the Essay (b) in projectional direction (y,y'). Essay On Fluoride Ion-Selective Electrodes! The rms-emittance of the beam is made to Building and Using Teams in the, match rms (e). After iterating trajectories (through a special object), electric potential and Essay on Fluoride space charge are recorded in the convergence.dat le; at the end of the simulation process this le can be found in the same folder where the source code is. If setted true in the beginning, it starts the of Integrity last phase, the plotting one; this is the on Fluoride list of all the plots produced: ' particle traces in Building Teams Workplace the geometry eld; ' zoom of particle traces in the range 0 '' 1 mm (the zone including the skimmer and the focus point); ' electric potential as a function of x, usually a curve starting near 0 (the skimmer is grounded but there is the plasma potential contribution) and ending at ''2000 V (the lens voltage); ' a 3D plot representing the electric potential as a function of x and y in the skimmer region; ' emittance at 50 mm, as a function of y and Essay Ion-Selective the angle y0, reporting the values of , , and ; 39 ' charge density (in C/m3) as a function of x; it is maximum at the beginning - at the skimmer tip -, then rapidly drops to lasswell's definition, zero, with a peak in correspondence to the focus point; ' space charge as a function of x and Ion-Selective y in the skimmer region; ' kinetic energies (in eV) of ying particles, in a scatter plot, as a func- tion of Essay, particles mass; ' signal intensity, in arbitrary units, for each mass, at Essay 8, 50 and 56 mm; ' beam prole histogram plot at psycho shower 4 and Essay Ion-Selective Electrodes 50 mm; ' a scatter plot for the beam prole, representing the y value as a func- tion of the particles mass, both at 50 and 56 mm.

40 Chapter 6 Simulation 6.1 Task 1 - solver. The rst task was to nd and Alzheimer’s Essay compare the dierent available solvers, in order to nd out which one is the fastest. With this aim, the computing time for 1 and 2 iterations has been determined, using one thread only and considering an Essay on Fluoride, Argon beam with 20k particles, a beam current of 1 mA and a mesh size equal to 100 m. The outcome of this comparison is the definition of politics bar plot in Figure 6.1. As it can be seen, the UMFPACKSolver is the fastest. Essay On Fluoride Ion-Selective Electrodes! Moreover this solver can also use multi-thread; this feature makes the UMFPACKSolver the more suitable;1 accordingly, it was used throughout the entire project. 6.2 Task 2 - computing time vs mesh size.

As explained in the previous chapter, to calculate the and Using Good in the electric potential and the charge density, IBSimu divides the on Fluoride Ion-Selective Electrodes simulation domain in small cells, with uniform size: for each cell UMFPACKSolver solves the problem, i.e. Psycho Shower Music! Poisson's dierential equation, and Essay on Fluoride Electrodes returns a value. So the mesh size has a large eect on the quality of the approximation: the smaller the mesh size, the higher the apocalypse now meaning quality of the on Fluoride Electrodes simulation is (down to the limit of mesh_size '' 0, representing the exact solution of the problem). The trouble is that it is impossible to decrease the mesh size innitely. The limits are the available memory (with 8967201 nodes - equivalent to a 10 m mesh size - the system reports a memory allocation error) and the computing time. Alzheimer’s Disease Essay Examples! In fact, the higher the number of nodes, the longer is the time needed to Ion-Selective Electrodes, solve the problem. So it is useful to mccandless into, nd a compromise to solve the problem with a good approximation and in a relatively short time. The relation between computation time and mesh size was investigated for mesh sizes in the range of Essay on Fluoride Electrodes, 15 '' 300 m.

In Table 6.1 and Figure 6.2 the data are given and plotted for a 20k particles Argon beam, with a current beam of 20 mA and 41 iterations. 1Twelve threads were available on the computer used. 41 Figure 6.1: Computing time for dierent solvers. Table 6.1: Computing time for dierent mesh sizes mesh (m) no of nodes time (s) 300 10197 77.85 250 14625 97.61 200 22761 131.92 150 40303 163.45 100 90321 259.35 50 359841 619.59 40 561801 853.01 30 997957 1343.57 25 1436481 2021.08 20 2243601 3608.08 15 3987023 8676.87 42 Figure 6.2: Computing time as a function of the number of nodes. It seems that the Building Teams data points plotted have 2 dierent trends: the Essay on Fluoride Electrodes rst data can be tted with a root function, then (from the now meaning 50 m mesh) the data can be tted with really good approximation through a square function. On Fluoride Ion-Selective Electrodes! The functions used to t the two curves are respectively y = a (1 + x) b (Figure 6.3) and y = A + B x + C x2 (Figure 6.4); (6.1) for the rst curve a = 0.32399, b = 0.59039, for the second curve A = 390.06724 , B = 6.03498 10''4 and C = 3.71075 10''10. Psycho! As the adjusted R2 are, respectively, 0.99772 and 0.99998 these could be considered good ts. As explained before, the mesh size has an impact on the quality of the Ion-Selective Electrodes results: a too large mesh could lead to a simulation not well representing the reality. In Figures 6.5 and 6.6 beam proles at 50 mm for dierent mesh sizes are plotted; this trend has been used as judging parameter to test the quality of the results. A brief description of the beam prole evolution from the nest mesh to the coarser one is provided, comparing each one with the former. Because 15 m is the smallest mesh size that can be used, the lasswell's definition 15 m prole has been taken as the plot which best represents the beam prole.

All the Ion-Selective Electrodes other plots, obtained increasing the mesh size, will be compared to this one. The main task is to reach a good compromise between the beam representation quality and of politics the computing time: it is useful to nd a minimum number of Essay Ion-Selective Electrodes, nodes which would guarantee a good nal result to attain the time optimization. Examples! In the following (through a dierent geometry) the beam prole was tted with a nonlinear function, taken from the models 43 Figure 6.3: Fit for the rst six points plotted in Ion-Selective Figure 6.2. Figure 6.4: Fit for the second part of the data plotted in lasswell's definition of politics Figure 6.2. 44 Figure 6.5: Beam proles for mesh sizes between 15 and 50 m. Figure 6.6: Beam proles for mesh sizes between 100 and Essay Ion-Selective Electrodes 300 m. 45 available in chris mccandless Origin. Essay On Fluoride Ion-Selective! Before starting the analysis it is important to underline that every plot is symmetrical due to the applied geometry: the code creates only the upper half of the simulation eld (i.e. the interfaces and the lens) and then it reects all the elements through a mirror function.

Considering the rst four beam proles (mesh sizes from 15 to 30 m) one can note that there are no meaningful dierences: increasing the mesh size in this range the beam prole is Teams in the Essay unaected. As there are small dierences, the number of counts could be considered constant: the dierence between the 15 m and the 30 m plot counts is less than 0.2%. On the contrary, increasing the mesh size to 40 m, considerable dierences appear: even if the total number of counts is nearly equal, the curve clearly shows an atypical evolution when approximating to the center. A sharp increase occurs in the very central range: the percentual dierence between the number of counts at Essay Ion-Selective Electrodes 0.25 mm and shower the one at 0.75 mm is about 22%. Electrodes! Further increasing the mesh size the Building Good in the Workplace Essay result becomes more pronounced: the total number of counts decreases (till the dierence with the nest mesh is greater than 31% - for on Fluoride, the 300 m mesh) and apocalypse also the shape changes. In the 100 m plot there is a very high central peak (the ratio between this peak and the 15 m peak is more than 1.5), so the trend is already much dierent. Considering coarser approximations, the outer peaks trend becomes more uniform, while the central one broadens and then splits in two dierent peaks (in the on Fluoride 300 m histogram the and Using Good in the Workplace Essay central counts number is very low). In short, large mesh sizes produce unrealistic results and on Fluoride Ion-Selective have to be avoided.

In conclusion the best compromise between quality and computing time is represented by psycho the 30 m mesh. Essay! As it has been shown before, approxi- mately 22 minutes are requested for Building and Using in the Essay, this geometry (for a 20k particles Argon beam with a current of Essay on Fluoride Ion-Selective Electrodes, 20 mA and 41 iterations). Furthermore, the Disease space charge density was calculated (data not shown). With increasing mesh size, almost nothing changes close to the skimmer orice. But a peak between. 0.01 and Essay 0.02 m - where the beam is focused - decreases when larger mesh sizes, until it disappears at 50 m. The ratios between the peak height for three medium meshes, 30 m, 40 m and psycho music 50 m, and Essay on Fluoride Ion-Selective Electrodes the smaller mesh used are 60%, 48% and 40%, respectively. Looking for a compromise, the former choice of The Importance of Integrity, a 30 m mesh size can be considered a good solution.

6.3 Task 3 - full 2D geometry switching. As the 2D mirrored geometry could not be considered a good representation of the simulation area (some troubles arise for Ion-Selective, particles traveling on the x axis), the third task was to modify the code in lasswell's of politics order to dene a 2D full geometry. This conguration is on Fluoride Ion-Selective not using the mirror function anymore, as the interfaces and the lens are completely dened. After the switch to psycho shower music, this new geometry, some simulations were run in order to compare the new computing time with the former one. Table 6.2 shows the time for both geometries. On Fluoride Ion-Selective! It is important to underline that with the same mesh size the full geometry has a doubled number of nodes with respect to the mirror 46 Table 6.2: Computing time for 2D mirror and full 2D geometry 2D mirror full 2D mesh (m) no of nodes time (s) no of lasswell's, nodes time (s) time ratio 300 9956 77.85 24889 161.90 2.0 250 14336 97.61 35840 211.69 2.1 200 22400 131.92 56000 292.98 2.1 150 39822 163.45 99556 385.92 2.3 100 89600 259.35 224000 620.14 2.3 50 358400 619.59 896000 1493.79 2.4 40 560000 853.01 1400000 2164.20 2.5 30 995556 1343.57 2488889 4239.65 3.1 25 1433600 2021.08 3584000 7784.64 3.8 one, because the electrodes and Essay on Fluoride Ion-Selective Electrodes the simulation eld are dened in the lower part too.

These values are referred to a 20k particles Argon beam, with a beam current of 10 mA and 41 iterations. The last column displays the ratio between the time taken by the full 2D geometry and Disease Essay the 2D mirror. The data ouput was used to evaluate the beam prole for the smaller mesh sizes (50 m, 40 m, 30 m and 25 m). On Fluoride Ion-Selective! The dierence between the full 2D and the 2D mirror beam proles gets obvious: they are no more com- pletely symmetrical, because particles are sent randomly. The member func- tion used in into the wild these rst simulations was add_2d_KV _beam_with_emittance(). It adds a 2D beam with dened KV emittance (KV stands for Kapchinsky- Vladimirsky, whose distribution is used for the beam spread in the projec- tional space). It becomes clear that the perfect beam symmetry could be achieved only Essay Ion-Selective with a large number of and Using, particles. Analyzing the number of counts in the two sections (the left and the right one) of each plot, it results that the percentual dierence is Ion-Selective less than 1%; moreover the bias is anti correlated to the mesh size: 0.54% for 25 m, 0.45% for 30 m, 0.27% for. 40 m, 0.09% for The Importance, 50 m. Essay On Fluoride Ion-Selective! In order to Disease Essay, compare the beam prole obtained with the two dierent geometries, one simulation with a 100k particles Ar- gon beam, with a current of 10 mA and a 30 m mesh size was used. The comparison with the corresponding 2D mirror result is displayed in Figure 6.7.

The dierences can be summarized in the following way: rst of all, even if the trend at the edge is similar, the midmost increasing is larger in the full 2D case. Moreover, the Electrodes number of central counts is psycho music much higher in the full 2D case: the ratio between the peak heights is about 1.2 and the percentual dierence of the total number of counts between 2D mirror and full 2D curve is about 19%. This result shows the Essay Ion-Selective Electrodes importance to switch to the new geometry; in fact it clearly proves that the mirror 2D case was aected by some errors in the trajectories calculation for particles in the center of the chris the wild beam, the region we are mostly interested in. Finally, some attempts have been done to t the full 2D beam prole 47 Figure 6.7: 2D mirror - full 2D beam prole @ 50 mm comparison. (using the data obtained with the 30 m mesh) with a known distribution: as the Gauss t had a R2 adjusted of only 0.99134, it has been chosen a Lorentzian t, obtaining a better result (R2 adjusted = 0.9963). This t is displayed in Figure 6.8. Olney, Chen and Douglas [30] measured gas ow proles downstream the skimmer using an impact pressure probe. On Fluoride! It consisted of a small 0.254 mm diameter orice in a at plate at the end of a 6.35 mm od tube that was connected to a pressure gauge. The gas ow proles were measured for an interface arrangement with a rst stage pressure (P1) of Alzheimer’s examples, 3.3 Torr and a sampler-skimmer spacing of 6.4 mm; this interface is similar to that used on commercial ICP-MS systems.

Using French calculations [47], they found the density o the on Fluoride Ion-Selective centerline: n(r, ') n0 = B cos 2 '' 2C r r0 ''2 (6.2) where ' is the apocalypse now meaning polar angle between the centre axis and the point of interest, r0 the orice radius, r the distance of the probe from the source (r2 = x2 p +z 2 p , where zp is the distance of the probe from the centerline) and on Fluoride Electrodes B and The Importance of Integrity C are, respectively, 0.643 and 1.365 (for Ar). Ion-Selective Electrodes! The impact probe was scanned radially across the beam at 13 mm down- stream the skimmer; Figure 6.9 shows the free jet gas ow prole obtained from impact pressure measurements made at several distances from the centerline. Considering the geometry and settings dierences between the case on study and the work by and Using Good Teams Essay Olney, Chen and Douglas, the beam prole obtained with IBSimu is consistent with the one shown in their work. On Fluoride Electrodes! 48 Figure 6.8: Lorentz t. Figure 6.9: Free jet proles calculated - dotted line - and Building Teams Workplace Essay measured - lled circles; the density eld of equation 6.2 is multiplied by an additional factor. cos' to account for Essay on Fluoride Ion-Selective, the decrease in the apparent area of the probe (solid angle) viewed from the source orice as the probe moves o-axis [30]. 49 6.4 Task 4 - Up and Te investigation. The optimum mesh size for a mirrored geometry was determined to be 30 m.

Since with a full 2D geometry the number of nodes doubles, some simulations have been done to lasswell's, see if a mesh bigger than 30 m guarantees good results. Essay! It has been found that using a 50 m mesh the beam prole does not change; so for the following task, this mesh size has been used. The aim was to analyze the eect of Disease, plasma potential (Up) and on Fluoride Electrodes electron temperature (Te) on the beam prole. Psycho Shower Music! These parameters have been chosen because they dene the plasma itself and they represent the main contribu- tion to the particles trajectories. After few simulations it became clear that it was necessary to change the particle seeding function; we soon realized that add_2d_KV _beam_with_emittance() did not take into account the on Fluoride charge density and apocalypse it was initializing the plasma potential to a Null value (no dierences were seen varying the Essay Ion-Selective plasma potential). However, the beam proles calculated in the former task were correct, because with such a high current beam the space charge eect was signicant. So, the new used function was add_2d_beam_with_energy(), which adds particles with kinetic energies sampled from The Importance of Integrity a gaussian distribution. Unfortunately, it was not possible with this new function to set a beam current greater than 5 A; for higher values, particles are grouped in Essay Electrodes bundles (needless to now meaning, say that this result can not be true). So, with a 100k particles Argon beam, a current of 5 A and 21 iterations (after having checked the con- vergence) some runs have been done with dierent plasma potential values: 0.1, 0.2, 0.5, 1, 2, 5, 8, 10, 15 and 20 V. The outcome beam prole does not have any signicative dierence until 1 V, then, increasing the plasma po- tential, the number of counts and on Fluoride Electrodes the peak height decrease. Moreover, above.

10 V all plots are almost identical, both in shape and number of counts; as a consequence it does not make sense to investigate low or high intervals and of Integrity the study was concentrated on the range 2 '' 10 V. This interval of survey is in a good agreement with the available literature data [13][18][19]. The trend shown in Figure 6.10 is Essay on Fluoride Ion-Selective probably due to the space charge eect: it becomes more intense with a higher potential, especially in the center of the beam, where the number of particles is high. Psycho Music! So, increasing. Up, more and more particles are lost on the skimmer walls; in a calculation for 10 V, this number could be near to 80% of the Essay Ion-Selective Electrodes total number of shower music, starting particles. Ion-Selective! With a low plasma potential value, some particles are colliding on the skimmer wall too, but this number is definition of politics smaller - with Up = 2 V it is about 40% - because the beam is spreading less than in Essay on Fluoride Electrodes the case of music, high Up. Regarding the charge density plot, its trend does not change. The only Ion-Selective dierence is in the peak corresponding to the focus point: its height halves from Good Teams Workplace 2 to Essay on Fluoride Electrodes, 6 V and psycho music then remains constant until 10 V. In conclusion of the plasma potential evaluation, one can say that the sharpest beam proles are achieved at lowest potential, in particular at Up = 2 V. A similar study has been conducted for the electron temperature, be- tween 2000 and Essay Electrodes 8000 K (corresponding to 0.259 and 1.035 eV, respectively, using the equipartition theorem). The number of lasswell's of politics, publications inquiring this 50 Figure 6.10: Beam proles for Te = 5000 K and dierent plasma potentials. topic is Essay on Fluoride considerable [18][26][32][35][36]; the Alzheimer’s Disease reported values range between. 1000 and 16000 K, depending on many factors (distance from the load coil, radial position, dry or wet plasma, introduced analyte and radio frequency power setting). The results for dierent plasma potentials (summarized in Figures 6.11 and 6.12) show a dierent behaviour. At low Up, increasing the electron temperature results in a rise of counts at the boundaries and a decrease in the center.

Probably due to a greater thermal agitation, the beam prole becomes smoother (this attening is more uniform than the one obtained increasing Up). Essay Ion-Selective! On the contrary, if the potential is high the plot is Teams in the Workplace Essay already at and by varying the temperature nothing changes. The best solution would be having a sharp peak (like the one obtained for the lower temperature) with a high number of counts (as it happens for Essay on Fluoride Electrodes, high Te). So choosing the best electron temperature is Alzheimer’s Essay not easy: both 2000 and 8000 K could be considered good solutions. Essay On Fluoride Ion-Selective! In the charge density plot, increasing the electron temperature, the of Integrity peak corresponding to the focus point moves slightly toward the skimmer, while its intensity increases and the full width half maximum (FWHM) gets smaller. These changes are small, so they could be neglected. The best conguration would be a focus point far away from the on Fluoride Ion-Selective Electrodes skimmer, in order to minimize the space charge eect. In order to better understand how the plasma potential and the electron temperature aect the chris mccandless simulation and, above all, to nd the Essay combination that gives the best result, three 3D plots have been done, representing the total number of counts, the peak height and the FWHM as a function of the two fundamental parameters. Lasswell's Definition Of Politics! The results are depicted in Figures 6.13 51 Figure 6.11: Beam proles for Up = 2 V and dierent electron temperatures. Figure 6.12: Beam proles for Up = 6 V and Ion-Selective Electrodes dierent electron temperatures. 52 Figure 6.13: Number of counts as a function of Up and psycho shower music Te. to Essay Electrodes, 6.15.

As evaluated before, it was shown that Up = 2 V is the best plasma potential. Regarding the electron temperature, two dierent values could be good: with Te = 2000 K the peak is narrow (lowest FWHM) and his height is maximum. On the other hand, with Te = 8000 K there is still a good FWHM and the number of counts is increased. The good quality of these two combinations (Up = 2 V - Te = 2000 K and Up = 2 V - Te = 8000 K) is underlined in the plot represented in Figure 6.16, obtained with a combination between number of counts and FWHM. From the literature review it can be postulated that 2000 K is now meaning a too low value for the present case.

In fact the electron temperature in a Fassel torch is around 10000 K and the plasma bulk properties remain unchanged as it proceeds through the sampling orice [19]; the only signicant electron loss at the walls of the Essay sampling plate is conned to distances of the order of Good Workplace Essay, one Debye length - 10''2 to 10''3 mm. In conclusion for the next simulations the following values were adopted: Up = 2 V and Te = 8000 K. 6.5 Task 5 - dierent masses. Once completed the Argon beam simulations, the next step was to intro- duce other particles, to Essay on Fluoride Electrodes, see the particles beam prole. Since the plasma is constituted by Argon, the number of the other masses is so low that their contribution to the electric potential is nearly negligible. So, to speed up the chris simulation, it was convenient to Essay on Fluoride Ion-Selective, simulate only Argon in the rst runs 53 Figure 6.14: Peak height as a function of psycho shower music, Up and Te. Figure 6.15: Full width half maximum as a function of Up and Te. 54 Figure 6.16: (number of counts)2 / full width half maximum. (to calculate the resulting electric potential) and then, in the last part, all the other particles. This topic will be discussed in detail in the next section.

The rst set of simulations was aimed to study how the Essay on Fluoride Electrodes number of counts is lasswell's aected by the mass of the projectile at dierent potentials. The array of particles used (excluding Ar) was: 1, 5, 10, 20, 30, 50, 60, 80, 100, 140, 180, 220 , 260, 300 amu. 100k particles per species were seeded, with a 50 m mesh, Te = 8000 K and for dierent plasma potentials: 2, 3, 4, 6, 10 V. The signal intensity per species, downstream the lens orice, is given in Figure 6.17. On Fluoride Ion-Selective Electrodes! The trend obtained is logarithmic for each potential, even if with in- creasing Up the curves are attening. A good t has been found: the curve.

y = a''bln(x+c) always provides R2 adjusted greater than 0.999. Compar- ing the plot in Figure 6.17 with the one obtained at 50 mm (just before the lens orice) and shown in Figure 6.18 clearly indicates that a lot of particles are lost on of Integrity Essay the lens walls, as the maximum intensity halves. Moreover, the most intense lost is for low mass particles: considering the intensity ratio between 50 and 56 mm, it passes from 7.57 for m=1 to Essay on Fluoride, 3.87 for m=100 to 2.08 for m=300. This could mean that lower masses are mostly at the boundary of the beam - whilst higher masses are in the centre - or that the spread is higher for light particles - making the prole nearly at. In the The Importance following this particular distribution was studied through the beam prole plots. Considering instead the on Fluoride Ion-Selective signal intensity per species for dierent electron temperatures, the curves are not aected and apocalypse the intensity dierence is nearly negligible (see Figure 6.19). Increasing the electron temperature, the 55 Figure 6.17: Signal intensity per mass @ 56 mm for Te = 8000 K and dierent plasma potentials.

Figure 6.18: Signal intensity per mass @ 50 mm for Te = 8000 K and dierent plasma potentials. 56 Figure 6.19: Signal intensity per mass @ 56 mm for on Fluoride Ion-Selective Electrodes, Up = 2 V and dierent electron temperatures. number of counts also increases, in a non linear way: higher the mass, bigger the dierence from two dierent temperatures is. Nevertheless the into the wild gap is on Fluoride Ion-Selective Electrodes quite small: for Essay, m=300, the percentual dierence between 5000 and 12000 K (in respect to the lower Te) is Essay about 6. The eect of an electron temperature changing on the number of counts for m=300 is shower music shown in Figure 6.20. Essay On Fluoride Ion-Selective Electrodes! In order to see in detail how plasma potential and of politics electron temper- atures aect the beam prole, some simulations have been run with the three masses (in addition to Ar) which give an overall view on all possible particles: 1, 150, 300. The result is consistent with the one obtained in case of Argon: it validates 2 V as the best plasma potential and the trend for dierent Te is equivalent to on Fluoride Ion-Selective Electrodes, the one showed in the previous section. As it resulted from signal intensity plots, the Alzheimer’s Disease number of counts for lower masses is low. Running the same number of particles would make a comparison between beam proles of mass 1 and Essay Electrodes 300 impossible: the former one would be completely at compared to the other. As the beam prole evolution (changing Up and Te) is the same for mass 40, 150 and 300, it is reasonable to presume this trend is identical for mass 1. The beam prole was studied in detail for dierent electron temperatures (Figure 6.21). As it is The Importance of Integrity shown for m=150, increasing Te, the central peak decreases and broadens until 6000 K, then, it starts increasing again. On Fluoride Electrodes! Moreover, while its central width does not change, the boundary number of counts progressively decreases and so the transition from the boundary to the centre becomes sharper (the area under the curve being constant). The only dierence with 57 Figure 6.20: Signal intensity @ 56 mm for m = 300 and dierent electron temperatures.

Figure 6.21: Beam prole @ 50 mm for Up = 2 V, m = 150 and dierent electron temperatures. 58 Figure 6.22: Beam prole @ 50 mm for Building Good Teams, dierent masses, for Up = 2 V and. Te = 8000 K. argon is right in this area: in the analyzed case the boundary number of counts drops to zero (this feature is even more noticeable for m=300) at about 4 mm from the centre, giving to the prole a more sharp shape. Ion-Selective Electrodes! This phenomenon has been more deeply investigated. With a set of projectile similar to the one used for the rst plots, the beam prole for Workplace Essay, each species has been represented - for Up = 2 V and. Te = 8000 K. For low masses it was necessary to run more particles in order to have a good statistics. Especially in this plot the mass discrimination is obvious: most of the low species are lost on the skimmer and lens walls, so their contribute is about one order of magnitude smaller for high masses. As observed before the beam prole progressively changes: while Argon (previously studied) can be tted with a lorentzian curve, increasing the mass, the prole loses its tails and acquires a better dened shape.

Starting from m = 160, the boundary number of counts drops to zero; in other words, high masses are well focused. This is an important result, because it means that all these particles will pass through the lens orice. To better visualize the results it was convenient to represent the beam prole ratio between a given mass and Ion-Selective mass 120. This value was choosen because its curve is the rst having nearly zero counts at the edge. As in the analyzer enters just the central part of the Essay beam, high boundary ratios were not take into account. The plot in Ion-Selective Figure 6.23 clearly shows the mass discrimination as a function of Alzheimer’s Disease examples, atomic mass and radius (radial distance from the beam center - dened as 0.02 m). On Fluoride Ion-Selective! This plot underlines how much sharper the beam proles are for mccandless into the wild, high 59 Figure 6.23: Counts ratio @ 50 mm for Essay Ion-Selective Electrodes, Up = 2 V and Te = 8000 K. masses: it is important to notice that the resulting hollow for low masses does not mean the Alzheimer’s examples total number of Essay on Fluoride Electrodes, counts in the center is lower than at the boundaries, but just that the number of counts is increasing slower (to the centre) for low than for high masses. In The! 6.6 Task 6 - iteration settings. As anticipated, with many projectiles it is convenient to split the iteration phase in two parts: in the initial runs only on Fluoride Electrodes Argon is now meaning seeded, while in the last all the other particles (dened in on Fluoride Electrodes the masses array) are added. In fact the one that contributes more to the total electric potential is Argon, while other particles have a negligible impact on it. Some simulations have been run to answer the following questions: ' With a xed number of chris into the wild, iterations, does the beam prole change vary- ing the number of initial and nal iterations' How' Is the computing time aected' ' How many particles are needed to y in the last run(s) in order to Essay Ion-Selective, have a good compromise between a good beam prole and a short computing time' ' How many particles are optimal for the rst runs' The rst comparison was aimed to see which changes occur when the number of iterations in which all particles are sent vary.

With a xed 60 Figure 6.24: Electric potential dierence as a function of iteration number for now meaning, the analyzed cases. number of Essay on Fluoride Electrodes, total iterations (25), dierent combinations have been tried: (case 1) 10+15, (case 2) 15+10, (case 3) 23+2, (case 4) 24+1. Good Teams In The Essay! The rst parameter checked was the electric potential convergence: in Figure 6.24 the electric potential dierence is shown for Ion-Selective Electrodes, the considered cases. There are two points that have to be underlined: (i) the y axis has a logarithmic scale - this means that the initial decrease is sharp - and (ii) in case4 the electric potential dierence is Disease Essay examples not calculated after ying all parti- cles - because in Essay on Fluoride the code the particles are sent after the electrical potential is recalculated. 2 The increase in each curve is due to Disease, the addition of other species: considering that the total electric potential is 2000 V, this oper- ation does not signicantly aect the result. To validate this hypothesis, the Essay Ion-Selective obtained beam proles have been compared to music, the one obtained in the rst case.

With 15 + 10 iterations the on Fluoride Electrodes result is lasswell's definition identical (exactly the Ion-Selective Electrodes same number of counts per interval) to the rst one, while case 3 and chris mccandless into 4 have some small dierences, even if the prole shape remains unchanged. As the com- puting time decreases from 34 (case1) to 29 (case2) to 19 minutes (case4), the conclusion is the following: reducing the number of nal iterations does not signicantly aect the nal result; the dierence is negligible in all cases even for particles with low mass - in which case the total number of counts is low. This result has been validated also in the case of 20k particles in Essay on Fluoride Ion-Selective the rst runs and 100k in the last one. Then, two simulations with a dierent nal number of particles have been performed: 50k and 100k. Shower Music! For low masses (m=1 in Essay on Fluoride Ion-Selective Electrodes the analyzed 2So case4 represents the convergence for Ar only. Apocalypse! 61 Figure 6.25: Ratio between the beam prole @ 50 mm with 50k particles and the one obtained with 100k particles, for m=1. case) the number of particles reaching the Essay on Fluoride Ion-Selective Electrodes end of the simulation eld is low and random uctuations aect signicantly the beam prole. As the uctuation amplitude does not change passing from the apocalypse now meaning rst to the second case, the former one represents a coarse approximation (as clearly indicated in Figure 6.25). Increasing the atomic mass the number of counts increases too and the background noise becomes negligible. So it is on Fluoride better to split the following discussion in two cases. Lasswell's Definition! For high masses the solution is Essay on Fluoride Electrodes likewise the prece- dent: running with 50k instead of 100k particles is a good approximation and the advantage is that the simulation time is reduced - halved in The Importance Essay the case of 10 + 15 iterations.

To see how much time is earned running less particles in the last run only, two simulations have been done, with 50k particles at the beginning and 50/100 in the last run. The dierence is about 15%, but is not really signicant as the total time needed is around 20 minutes (19 min in on Fluoride Electrodes the rst case and 22 min in the second). Apocalypse Now Meaning! The situation is critical for low masses: running few particles in the last run(s) does not provide a good statistics. Therefore, it is convenient to run more particles (in the last run only), even if it takes a bit more time, to have a better statistic. Essay On Fluoride Electrodes! To conclude this study, the last parameter to change was the psycho shower number of on Fluoride, particles in the rst runs: 3 the simulation result for 20k particles was compared to Alzheimer’s, the one obtained for 50k - with 100k particles in Essay on Fluoride Ion-Selective the last runs 3A variation in the number of Argon particles does not change the total charge density (it is dened as constant); the only quantity changing is the charge density carried by apocalypse each particle. Essay Ion-Selective! 62 - rstly for 10 + 15 and then for 24 + 1 iterations. In both cases there are no dierences between the two simulations - for the case 10 + 15 iterations every single beam has the The Importance Essay same amplitude as in the other case and similarly for 24 + 1 iterations. In the rst case even the computing time does not importantly change, probably because the time needed to seed only Argon is Essay on Fluoride Ion-Selective Electrodes smaller compared to the one for all particles.

On the contrary, the dierence is notable in the second case: instead of 22, just 14 minutes are needed. Anyway, it is important to underline that this is not a general result: sending more species, the time needed for the last iteration will increase, while the time for Argon does not change. So the percentual time earned will decrease with the total number of species increasing. Anyhow decreasing the number of Disease Essay examples, Argon particles does not aect the beam prole quality, so it can be reduced to 20k. The following list summarizes the settings that optimize both the results quality and the computing time: ' number of iterations: 24 + 1; ' number of particles in the last run: 100k; ' number of particles in the rst runs: 20k. 6.7 Task 7 - Cadmium. In order to Electrodes, compare between simulation and Good Essay experimental results, Cd can be used, with three of its isotopes: 110, 111 and 114. Through this com- parison it is possible to nd out the Ion-Selective plasma fundamental parameters that characterize the used instrument. In the following a short experimental description of the lasswell's implantation and measure of ions number is given.

In order to detect the radial distribution of Cd - this element is Essay on Fluoride Ion-Selective used because it shows a signicant radial dependence -, an Aluminium target was placed at Building and Using Good Teams in the Workplace the base of the extraction lens. On Fluoride Electrodes! Thus implanted ions should represent the spatially resolved composition of the extracted ion beam. The target is analyzed by Laser Ablation ICP-MS after implantation, performing a line scan from the rim region (A) toward the center of the lasswell's definition target (B), as shown in Ion-Selective Figure 6.26. The spacing between two adjacent ablation spots (150 m) is sucient to apocalypse, have a high spatial resolution density and, in the same time, to avoid overlapping [43]. Essay On Fluoride Electrodes! Because laser ablation removes material in the range of apocalypse now meaning, several hundreds of nanometer per pulse, a complete removal of the im- planted ions is Ion-Selective Electrodes ensured. The calculated ratio 114Cd/111Cd in a single data set from a representative Cd isotope ratio analysis is chris mccandless into represented in Essay Ion-Selective Figure 6.27, with the corresponding transient signal for 114Cd. Teams Workplace Essay! Since laser ablation provides spatially resolved information on the im- planted matter, a relation between Cadmium signal and ion beam intensity has to be assumed in order to deduce the ion beam prole. However, the sputtering due to the high Ar-beam current jeopardizes this relation; the 63 Figure 6.26: Sketch of the Al target assembly mounted in the Neptune MC- ICP-MS instrument. The dotted line denes the Ion-Selective area exposed to the ion beam and apocalypse now meaning the position of the line scan is given by the black line [43]. Essay On Fluoride Electrodes! Figure 6.27: 114Cd/111Cd isotope ratio (open circles) and signal intensity [43]. 64 Table 6.3: Set of simulation run run number Up (V) Te (K) 1 2 8000 2 3 5000 3 4 10000 4 8 5000 5 2 5000 6 2 10000 signal intensity is high in an annulus around 1 mm from the centre and then decreases when moving toward the centre.

This drop coincides with optically observed material defect; at this location the low signal is probably caused by removal of material by sputtering. To plot the ratio 114Cd/111Cd against the distance from the centre, some simulations have been run, with the following conguration set: ' 35 iterations, 20 with Argon only + 15 with all the particles, ' masses array = 110, 111, 114, ' beam current = 5 A, ' mesh size = 50 m, ' dierent plasma potentials (Up) and electron temperature (Te). As explained before, the aim of these simulations was to nd a beam prole as similar as possible to the one shown in Figure 6.27. To reach this achievement, Up and Te were varied in into the wild their validity interval. The parameters for Electrodes, each run are summarized in Table 6.3. Beam proles have been plotted; increasing Up the trend becomes at, so Up = 2 V is the setting that resembles the real value best. Examples! Regarding the electron temperature, its contribute is not signicant as the Up is. Since the Essay Electrodes ratio obtained with the simulation is slightly dierent from the experimental one, identifying the electron temperature real value results more dicult. In Figures 6.28 to 6.30 ratios are given for three values of Te. It seems that the intermediate case - 2 V and 8000 K - is the closer to reality, even if the Alzheimer’s Essay examples shape diers for some features.

While the experimental plot rapidly decreases in the center and its trend is clear, the simulated one decreases slowly; at the edge, it can be seen the Essay on Fluoride Electrodes same low point it can be found at psycho music 6 mm in Figure 6.27 - even if in Ion-Selective Figure 6.29 is at dierent position, 2 mm closer to the center. The trouble is that data processing could give rise to dierent explanations, depending on which bin size is Alzheimer’s Disease choosen plotting the histogram. More accurated and resoluted simulations are necessary in on Fluoride Ion-Selective order to make this comparison more precise and reliable. 65 Figure 6.28: 114Cd/111Cd ratio for Up = 2 V and Te = 5000 K. And Using Essay! Figure 6.29: 114Cd/111Cd ratio for Up = 2 V and Te = 8000 K. 66 Figure 6.30: 114Cd/111Cd ratio for on Fluoride, Up = 2 V and Te = 10000 K. 67 Chapter 7 Results and discussion The present work wants only to be a starting point in the understanding of the extraction process: in of Integrity the future, on one hand more simulations and with dierent softwares can be performed and on the other some im- provements can be applied to the instrument.

IBSimu already represents a better simulation package compared to Essay Ion-Selective, SIMION; with the lasswell's of politics latter, taking into account the space charge eects is dicult and really impractical. Nev- ertheless, IBSimu still has a liability: it is impossible to y neutral particles and then simulating the scattering process between neutrals. Essay On Fluoride! For this rea- son the group of Kivel is developing new simulations, both with dsmcFoam1 and with PI-DSMC (Parallel Interactive Direct Simulation Monte Carlo). Both this programs use the probabilistic (Monte Carlo) simulation to under- stand the uidodynamics of the free jet expansion. DSMC has been already documented in some articles [38] [39]; the particular implementation of the algorithm is definition called FENIX. As the solver in IBSimu, the Monte Carlo al- gorithm models the Essay on Fluoride Ion-Selective gas ow by dividing the simulation region into small spatial collision cells, each one smaller in the extent than the local mean free path. Then, each particle is Disease examples given a random chance to collide with its nearest neighbor in its collision cell, using the collision statistics appropri- ate to the density and temperature in the cell. A more detailed description of the Essay Ion-Selective algorithm can be found elsewhere [38] [39]. Disease Examples! The aim of the FENIX simulation would be to make a more detailed calculation of the ow in the ICP-MS, not limited to the region downstream the skimmer anymore, but in the whole extraction interface. In this approach the study of the jet ex- pansion reported in chapter 4 is fundamental to make a comparison between simulated and theoretical results and in order to validate the Essay Ion-Selective model. This new simulation software is fundamental even for another reason: applying a modest voltage to of politics, the skimmer could improve the transmission eciency.

Usually about 10% of the total number of ying particles is lost on the skimmer walls and on Fluoride Ion-Selective Electrodes the trouble is that most of these particles are the lightest. Electrically oating one or both the The Importance of Integrity Essay cones at Essay Electrodes various potentials could accelerate the ions and therefore reduce this phenomenon. It has been found, with IBSimu, that having the skimmer at few volts would focus the Building Good Workplace Essay 1dsmcFoam is part of the Essay Ion-Selective open source CFD package OpenFOAM. The Importance! 68 Figure 7.1: Sketches of the three used arrangements [23]. beam; the downside of this action stands upstream the skimmer, where ions would see a repulsive force. For this reason simulating the entire extraction interface with DSMC is necessary, in Ion-Selective order to understand the beam behav- ior. Hu and Houk [23] applied modest DC voltages (+10 to +50 V ) to both the sampler and the skimmer or, alternatively, left the sampler oating - i.e., deliberately not connected to any voltage source or to ground - with the skimmer biased. Three specic arrangements (shown in gure 7.1) were studied: (a) sampler and chris mccandless the wild skimmer biased together, (b) sampler oated and skimmer biased and (c) sampler grounded and skimmer biased. Essay Ion-Selective! The results are depicted in psycho gure 7.2 with Co+ as analyte.2 There is an improvement in each case: by a factor of 4 (modestly) by applying the same DC voltages - about 20 V - to both sampler and skimmer (A), by on Fluoride Electrodes a factor 5 of in case C, and by a factor of 6 by oating the sampler and applying a DC voltage of psycho music, 30 '' 40 V to the skimmer. It results that conguration b is the one which gives the higher signal; 2Relative sensitivity refers to the sensitivity obtained for a given element with one of the new interface arrangements divided by that obtained for the same element with the conventional interface. 69 Figure 7.2: Relative Co+ sensitivity as a function of biasing voltage [23].

Table 7.1: Molar sensitivities for various elements expressed in terms of atomic concentration [23] molar sensitivity (counts/ (s mM)) interface arrangement Co Rh Ho m/z = 59 m/z = 103 m/z = 165 conventional interface 5.6 107 8.5 107 2.2 108 interface b 3.5 108 3.3 108 3.0 108 in Table 7.1 molar sensitivities for various elements are compared. Another advantage given by this conguration is the reducing of the mass bias: in on Fluoride fact, the sensitivity is improved for Co+ by a much greater factor than is in the case for the heavier Ho+. Even if it seems that the ions have a sucient kinetic energy to ow through the sampling cones, some simulations should been run in order to check what happens upstream the skimmer: applicating a positive potential could repel ions and Building and Using Essay prevent them from passing through the Essay on Fluoride Electrodes orice. So in this case the simulation eld has to be extended, in order to start the The Importance beam in correspondence to the sampler. 70 Chapter 8 Conclusions As explained in the introduction, the aim of this work was the optimization of the ion extraction from the ICP.

IBSimu turned out to be a suitable and useful instrument for on Fluoride Electrodes, this purpose, thanks to its versatility and easiness of use. It calculates the comprehensive electrci potential dividing the simula- tion region in small meshes or cells. Once chosen the fastest solver among the now meaning many available, the mesh size has been determined in order to have a good compromise between results quality and computing time. At the beginning, the code describing the Essay Electrodes simulation eld was characterized by a 2D mirror geometry; due to some problems, switching to a full geometry came out to be convenient. Apocalypse Now Meaning! Then the main section of the work started: the Essay Ion-Selective Electrodes investigation on how the beam prole changes upon varying the plasma main parameters, i.e. the plasma potential and lasswell's of politics the electron temperature. Changing the plasma potential, noticeable dierences were observed in the beam prole only in the range between 2 and 10 V; increasing Up more particles collide on the skimmer wall and Essay Electrodes then the beam prole decreases in intensity attening. The electron temperature has a less considerable eect and, particularly, its consequence depends on the plasma potential value: if Up is low, increasing. Te the lasswell's definition of politics trend attens, while if Up is high nearly nothing changes.

Since the aperture to the mass spectrometer is 4 mm wide, the couple of values. Up = 2V and Te = 8000K has been chosen in order to Essay on Fluoride Electrodes, have a sharp peak with a high number of music, counts. This result has been obtained ying only Argon ions, but it has then been ratied simulating a beam with many species. One of the on Fluoride most severe problem in the Inductively Coupled Plasma Mass Spectrometry is mass discrimination, that is the preferential lost of the beam particles with a low mass in The Importance respect to heavier species. This phenomenon has been characterized and then the eect of Essay on Fluoride Ion-Selective, a plasma potential and elec- tron temperature variation has been studied in Disease Essay order to see if it determines any advantage. While only small and negligible dierences occur changing. - caricare i tuoi contenuti.

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