Application of Ultraintense Lasers to validate materials for laser fusion: production of ions and other relevant species

Justification of the need and demand of experimental facilities to test and validate materials for first wall in laser fusion reactors - Characteristics of the laser fusion products - Current ?possible? facilities for tests Ultraintense Lasers as ?complete? solution facility - Generation of ion pulses - Generation of X-ray pulses - Generation of other relevant particles (electrons, neutrons..)

Kinetics of amorphization induced by swift heavy ions in α-quartz

The kinetics of amorphization in crystalline SiO2 (α-quartz) under irradiation with swift heavy ions (O+1 at 4 MeV, O+4 at 13 MeV, F+2 at 5 MeV, F+4 at 15 MeV, Cl+3 at 10 MeV, Cl+4 at 20 MeV, Br+5 at 15 and 25 MeV and Br+8 at 40 MeV) has been analyzed in this work with an Avrami-type law and also with a recently developed cumulative approach (track-overlap model). This latter model assumes a track morphology consisting of an amorphous core (area σ) and a surrounding defective halo (area h), both being axially symmetric. The parameters of the two approaches which provide the best fit to the experimental data have been obtained as a function of the electronic stopping power Se. The extrapolation of the σ(Se) dependence yields a threshold value for amorphization, Sth ≈ 2.1 keV/nm; a second threshold is also observed around 4.1 keV/nm. We believe that this double-threshold effect could be related to the appearance of discontinuous tracks in the region between 2.1 and 4.1 keV/nm. For stopping power values around or below the lower threshold, where the ratio h/σ is large, the track-overlap model provides a much better fit than the Avrami function. Therefore, the data show that a right modeling of the amorphization kinetics needs to take into account the contribution of the defective track halo. Finally, a short comparative discussion with the kinetic laws obtained for elastic collision damage is given.

Kinetics of color center formation in silica irradiated with swift heavy ions: Thresholding and formation efficiency

We have determined the cross-section σ for color center generation under single Br ion impacts on amorphous SiO2. The evolution of the cross-sections, σ(E) and σ(Se), show an initial flat stage that we associate to atomic collision mechanisms. Above a certain threshold value (Se > 2 keV/nm), roughly coinciding with that reported for the onset of macroscopic disorder (compaction), σ shows a marked increase due to electronic processes. In this regime, a energetic cost of around 7.5 keV is necessary to create a non bridging oxygen hole center-E′ (NBOHC/E′) pair, whatever the input energy. The data appear consistent with a non-radiative decay of self-trapped excitons.

Ionoluminescence as sensor of structural disorder in crystalline SiO2: determination of amorphization threshold by swift heavy ions

Ionoluminescence (IL) has been used in this work as a sensitive tool to probe the microscopic electronic processes and structural changes produced on quartz by the irradiation with swift heavy ions. The IL yields have been measured as a function of irradiation fluence and electronic stopping power. The results are consistent with the assignment of the 2.7 eV (460 nm) band to the recombination of self-trapped excitons at the damaged regions in the irradiated material. Moreover, it was possible to determine the threshold for amorphization by a single ion impact, as 1:7 keV/nm, which agrees well with the results of previous studies.

Ionoluminescence induced by swift heavy ions in silica and quartz: a comparative analysis

Ionoluminescence (IL) of the two SiO2 phases, amorphous silica and crystalline quartz, has been comparatively investigated in this work, in order to learn about the structural defects generated by means of ion irradiation and the role of crystalline order on the damage processes. Irradiations have been performed with Cl at 10 MeV and Br at 15 MeV, corresponding to the electronic stopping regime (i.e., where the electronic stopping power Se is dominant) and well above the amorphization threshold. The light-emission kinetics for the two main emission bands, located at 1.9 eV (652 nm) and 2.7 eV (459 nm), has been measured under the same ion irradiation conditions as a function of fluence for both, silica and quartz. The role of electronic stopping power has been also investigated and discussed within current views for electronic damage. Our experiments provide a rich phenomenological background that should help to elucidate the mechanisms responsible for light emission and defect creation.

Ultraintense lasers applied to laser fusion material testing: production of ions, X rays and neutrons

Due to the particular characteristics of the fusion products, i.e. very short pulses (less than a few μs long for ions when arriving to the walls; less than 1 ns long for X-rays), very high fluences ( 10 13 particles/cm 2 for both ions and X rays photons) and broad particle energy spectra (up to 10 MeV ions and 100 keV photons), the laser fusion community lacks of facilities to accurately test plasma facing materials under those conditions. In the present work, the ability of ultraintese lasers to create short pulses of energetic particles and high fluences is addressed as a solution to reproduce those ion and X-ray bursts. Based on those parameters, a comparison between fusion ion and laser driven ion beams is presented and discussed, describing a possible experimental set-up to generate with lasers the appropriate ion pulses. At the same time, the possibility of generating X-ray or neutron beams which simulate those of laser fusion environments is also indicated and assessed under current laser intensities. It is concluded that ultraintense lasers should play a relevant role in the validation of materials for laser fusion facilities.

Ultraintense Lasers Applied to Laser Fusion Material Testing: Production of Ions, X rays and Neutrons

The ability of ultraintese lasers to create short pulses of energetic particles and high fluences is addressed as a solution to reproduce ion and X-ray ICF bursts for the characterization and validation of plasma facing components. The possibility of using a laser neutron source for material testing will also be discussed.

Tailoring the Optical Properties of Silica Irradiated with Swift Heavy Ions

Irradiation with swift heavy ions (SHI), roughly defined as those having atomic masses larger than 15 and energies exceeding 1 MeV/amu, may lead to significant modification of the irradiated material in a nanometric region around the (straight) ion trajectory (i.e., latent tracks). In the case of amorphous silica it has been reported that SHI irradiation originates nano-tracks of either higher density than the virgin material (for low electronic stopping powers, Se < 7 keV/nm) [1] or having a low-density core and a dense shell (Se > 12 keV/nm) [2]. The intermediate region has not been studied in detail but we will show in this work that essentially no changes in density occur in this zone. An interesting effect of the compaction is that the refractive index is increased with respect to that of the surroundings. In the first Se region it is clear that track overlapping leads to continuous amorphous layers that present a significant contrast with respect to the pristine substrate and this has been used to produce optical waveguides. The optical effects of intermediate and high stopping powers, on the other hand, are largely unknown so far. In this work we have studied theoretically (molecular dynamics and optical simulations) and experimentally (irradiation with SHI and optical characterization) the dependence of the macroscopic optical properties (i.e., the refractive index of the effective medium, n_EMA) on the electronic stopping power of the incoming ions. Our results show that the refractive index of the irradiated silica is not increased in the intermediate region, as expected; however, the core-shell tracks of the high-Se region produce a quite effective enhancement of n_EMA that could prove attractive for the fabrication of optical waveguides at ultralow fluences (as low as 1E11 cm^-2). 1. J. Manzano, J. Olivares, F. Agulló-López, M. L. Crespillo, A. Moroño, and E. Hodgson, "Optical waveguides obtained by swift-ion irradiation on silica (a-SiO2)," Nucl. Instrum. Meth. B 268, 3147-3150 (2010). 2. P. Kluth, C. S. Schnohr, O. H. Pakarinen, F. Djurabekova, D. J. Sprouster, R. Giulian, M. C. Ridgway, A. P. Byrne, C. Trautmann, D. J. Cookson, K. Nordlund, and M. Toulemonde, "Fine structure in swift heavy ion tracks in amorphous SiO2," Phys. Rev. Lett. 101, 175503 (2008).

On the charged particle drag acting on LAGEOS

A recent study by the authors points to Charged Particle Drag (CPD) as a contributor to revisit in the LAGEOS non-gravitational perturbations problem. Such perturbations must account for dynamical contributions in the order of pms−2 . The simulated effect takes into account: (i) spatial and temporal variations of the plasmatic parameters (temperature and concentration of the species), (ii) spacecraft potential variations caused by both the eclipse passages and variations in the parameters mentioned above, and (iii) solar and geomagnetic conditions. Furthermore, recent theoretical improvements concerning scattering drag overcome previous limitations allowing for a complete formulation of this effect. For each satellite the lifetime CPD instantaneous acceleration is computed. The plasmatic parameters have been obtained fromthe Sheffield Coupled Thermosphere-Ionosphere-Plasmasphere (SCTIP) semi-empirical model (up to the polar region), as well as alytical/empirical approximations based on spacecraft measurements for the auroral and polar regions. Results show that maximum amplitudes for LAGEOSI are larger than those for LAGEOS-II: −85 pms−2 and −70 pms−2 respectively. This is due to the almost (magnetically) polar orbit configuration of the first, producing larger combinations of plasmatic parameter values. High solar activity has a huge impact in the resulting LAGEOS accelerations: it yields a perfect modulation of the resulting acceleration with maximum amplitudes up to a factor of 10 when comparing low and high activity periods. On the other hand, the impact of the geomagnetic activity results into a reduction of the effect itself, probably due to a decrease in the hydrogen concentration for high energy input periods. The acceleration results will be used in a refined orbit computation in a subsequent investigation.

Electrodynamic Tethers For Planetary And De-orbiting Missions

Nuevas aplicaciones tecnológicas y científicas mediante amarras electrodinámicas son analizadas para misiones planetarias. i) Primero, se considera un conjunto de amarras cilíndricas en paralelo (veleros electrosolares) para una misión interplanetaria. Los iones provenientes del viento solar son repelidos por el alto potencial de dichas amarras generando empuje sobre el velero. Para conocer el intercambio de momento que provocan los iones sobre las amarras se ha considerado un modelo de potencial estacionario. Se ha analizado la transferencia orbital de la Tierra a Júpiter siguiendo un método de optimización de trayectoria indirecto. ii) Una vez que el velero se encuentra cerca de Júpiter, se ha considerado el despliegue de una amarra para diferentes objetivos científicos. iia) Una amarra podría ser utilizada para diagnóstico de plasmas, al ser una fuente efectiva de ondas, y también como un generador de auroras artificiales. Una amarra conductora que orbite en la magnetosfera jovial es capaz de producir ondas. Se han analizado las diferentes ondas radiadas por un conductor por el que circula una corriente constante que sigue una órbita polar de alta excentricidad y bajo apoápside, como ocurre en la misión Juno de la NASA. iib) Además, se ha estudiado una misión tentativa que sigue una órbita ecuatorial (LJO) por debajo de los intensos cinturones de radiación. Ambas misiones requiren potencia eléctrica para los sistemas de comunicación e instrumentos científicos. Las amarras pueden generar potencia de manera más eficiente que otros sistemas que utlizan paneles solares o sistemas de potencia de radioisótopos (RPS). La impedancia de radiación es necesaria para determinar la corriente que circula por todo el circuito de la amarra. En un modelo de plasma frío, la radiación ocurre principalmente en los modos de Alfven y magnetosónica rápida, mostrando un elevado índice de refracción. Se ha estudiado la impedancia de radiación en amarras con recubrimiento aislante para los dos modos de radiación y cada una de las misiones. A diferencia del caso ionosférico terrestre, la baja densidad y el intenso campo magnético que aparecen en el entorno de Júpiter consiguen que la girofrecuencia de los electrones sea mucho mayor que la frecuencia del plasma; esto hace que el espectro de potencia para cada modo se modifique substancialmente, aumentando la velocidad de Alfven. Se ha estimado también la impedancia de radiación para amarras sin aislante conductor. En la misión LJO, un vehículo espacial bajando lentamente la altitud de su órbita permitiría estudiar la estructura del campo magnético y composición atmosférica para entender la formación, evolución, y estructura de Júpiter. Adicionalmente, si el contactor (cátodo) se apaga, se dice que la amarra flota eléctricamente, permitiendo emisión de haz de electrones que generan auroras. El continuo apagado y encendido produce pulsos de corriente dando lugar a emisiones de señales, que pueden ser utilizadas para diagnóstico del plasma jovial. En Órbita Baja Jovial, los iones que impactan contra una amarra polarizada negativamente producen electrones secundarios, que, viajando helicoidalmente sobre las líneas de campo magnético de Júpiter, son capaces de alcanzar su atmósfera más alta, y, de esta manera, generar auroras. Se han identificado cuáles son las regiones donde la amarra sería más eficiente para producir auroras. iic) Otra aplicación científica sugerida para la misión LJO es la detección de granos cargados que orbitan cerca de Júpiter. Los electrones de alta energía en este ambiente pueden ser modelados por una distribucción no Maxwelliana conocida como distribución kappa. En escenarios con plasmas complejos, donde los campos eléctricos en Júpiter pueden acelerar las cargas hasta velocidades que superen la velocidad térmica, este tipo de distribuciones son muy útiles. En este caso las colas de las distribuciones de electrones siguen una ley de potencias. Se han estudiado las fluctuaciones de granos cargados para funciones de distribución kappa. iii) La tesis concluye con el análisis para deorbitar satélites con amarras electrodinámicas que siguen una Órbita Baja Terrestre (LEO). Una amarra debe presentar una baja probabilidad de corte por pequeño debris y además debe ser suficientemente ligero para que el cociente entre la masa de la amarra y el satélite sea muy pequeño. En este trabajo se estiman las medidas de la longitud, anchura y espesor que debe tener una amarra para minimizar el producto de la probabilidad de corte por el cociente entre las masas de la amarra y el satélite. Se presentan resultados preliminares del diseño de una amarra con forma de cinta para deorbitar satélites relativamente ligeros como Cryosat y pesados como Envisat. Las misiones espaciales a planetas exteriores y en el ámbito terrestre plantean importantes retos científico-tecnológicos que deben ser abordados y solucionados. Por ello, desde el inicio de la era espacial se han diseñando novedosos métodos propulsivos, sistemas de guiado, navegación y control más robustos, y nuevos materiales para mejorar el rendimiento de los vehículos espaciales (SC). En un gran número de misiones interplanetarias y en todas las misiones a planetas exteriores se han empleado sistemas de radioisótopos (RPS) para generar potencia eléctrica en los vehículos espaciales y en los rovers de exploración. Estos sistemas emplean como fuente de energía el escaso y costoso plutonio-238. La NASA, por medio de un informe de la National Academy of Science (5 de Mayo del 2009), expresó una profunda preocupación por la baja cantidad de plutonio almacenado, insuficiente para desarrollar todas las misiones de exploración planetaria planeadas en el futuro [81, 91]. Esta circustancia ha llevado a dicha Agencia tomar la decisión de limitar el uso de estos sistemas RPS en algunas misiones de especial interés científico y una recomendación de alta prioridad para que el Congreso de los EEUU apruebe el reestablecimiento de la producción de plutonio-238, -son necesarios cerca de 5 kg de este material radiactivo al año-, para salvaguardar las misiones que requieran dichos sistemas de potencia a partir del año 2018. Por otro lado, la Agencia estadounidense ha estado considerando el uso de fuentes de energía alternativa; como la fisión nuclear a través del ambicioso proyecto Prometheus, para llevar a cabo una misión de exploración en el sistema jovial (JIMO). Finalmente, dicha misión fue desestimada por su elevado coste. Recientemente se han estado desarrollando sistemas que consigan energía a través de los recursos naturales que nos aporta el Sol, mediante paneles solares -poco eficientes para misiones a planetas alejados de la luz solar-. En este contexto, la misión JUNO del programa Nuevas Fronteras de la NASA, cuyo lanzamiento fue realizado con éxito en Agosto de 2011, va a ser la primera misión equipada con paneles solares que sobrevolará Júpiter en el 2015 siguiendo una órbita polar. Anteriormente se habían empleado los antes mencionados RPS para las misiones Pioneer 10,11, Voyager 1,2, Ulysses, Cassini-Huygens y Galileo (todas sobrevuelos excepto Galileo). Dicha misión seguirá una órbita elíptica de alta excentricidad con un periápside muy cercano a Júpiter, y apoápside lejano, evitando que los intensos cinturones de radiación puedan dañar los instrumentos de navegación y científicos. Un tether o amarra electrodinámica es capaz de operar como sistema propulsivo o generador de potencia, pero también puede ser considerado como solución científicotecnológica en misiones espaciales tanto en LEO (Órbita Baja Terrestre) como en planetas exteriores. Siguiendo una perspectiva histórica, durante las misiones terrestres TSS-1 (1992) y TSS-1R (1996) se emplearon amarras estandard con recubrimiento aislante en toda su longitud, aplicando como terminal anódico pasivo un colector esférico para captar electrones. En una geometría alternativa, propuesta por J. R. Sanmartín et al. (1993) [93], se consideró dejar la amarra sin recubrimiento aislante (“bare tether”), y sin colector anódico esférico, de forma que recogiera electrones a lo largo del segmento que resulta polarizado positivo, como si se tratara de una sonda de Langmuir de gran longitud. A diferencia de la amarra estandard, el “bare tether” es capaz de recoger electrones a lo largo de una superficie grande ya que este segmento es de varios kilómetros de longitud. Como el radio de la amarra es del orden de la longitud de Debye y pequeño comparado con el radio de Larmor de los electrones, permite una recolección eficiente de electrones en el régimen OML (Orbital Motion Limited) de sondas de Langmuir. La corriente dada por la teoría OML varía en función del perímetro y la longitud. En el caso de una cinta delgada, el perímetro depende de la anchura, que debe ser suficientemente grande para evitar cortes producidos por debris y micrometeoritos, y suficientemente pequeño para que la amarra funcione en dicho régimen [95]. En el experimento espacial TSS-1R mencionado anteriormente, se identificó una recolección de corriente más elevada que la que predecía el modelo teórico de Parker- Murphy, debido posiblemente a que se utilizaba un colector esférico de radio bastante mayor que la longitud de Debye [79]. En el caso de una amarra “bare”, que recoge electrones a lo largo de gran parte de su longitud, se puede producir un fenómeno conocido como atrapamiento adiabático de electrones (adiabatic electron trapping) [25, 40, 60, 73, 74, 97]. En el caso terrestre (LEO) se da la condición mesotérmica en la que la amarra se mueve con una velocidad muy superior a la velocidad térmica de los iones del ambiente y muy inferior a la velocidad térmica de los electrones. J. Laframboise y L. Parker [57] mostraron que, para una función de distribución quasi-isotrópica, la densidad de electrones debe entonces ser necesariamente inferior a la densidad ambiente. Por otra parte, debido a su flujo hipersónico y a la alta polarización positiva de la amarra, la densidad de los iones es mayor que la densidad ambiente en una vasta región de la parte “ram” del flujo, violando la condición de cuasi-neutralidad,-en una región de dimensión mayor que la longitud de Debye-. La solución a esta paradoja podría basarse en el atrapamiento adiabático de electrones ambiente en órbitas acotadas entorno al tether. ABSTRACT New technological and scientific applications by electrodynamic tethers for planetary missions are analyzed: i) A set of cylindrical, parallel tethers (electric solar sail or e-sail) is considered for an interplanetary mission; ions from the solar wind are repelled by the high potential of the tether, providing momentum to the e-sail. An approximated model of a stationary potential for a high solar wind flow is considered. With the force provided by a negative biased tether, an indirect method for the optimization trajectory of an Earth-to-Jupiter orbit transfer is analyzed. ii) The deployment of a tether from the e-sail allows several scientific applications in Jupiter. iia) It might be used as a source of radiative waves for plasma diagnostics and artificial aurora generator. A conductive tether orbiting in the Jovian magnetosphere produces waves. Wave radiation by a conductor carrying a steady current in both a polar, highly eccentric, low perijove orbit, as in NASA’s Juno mission, and an equatorial low Jovian orbit (LJO) mission below the intense radiation belts, is considered. Both missions will need electric power generation for scientific instruments and communication systems. Tethers generate power more efficiently than solar panels or radioisotope power systems (RPS). The radiation impedance is required to determine the current in the overall tether circuit. In a cold plasma model, radiation occurs mainly in the Alfven and fast magnetosonic modes, exhibiting a large refraction index. The radiation impedance of insulated tethers is determined for both modes and either mission. Unlike the Earth ionospheric case, the low-density, highly magnetized Jovian plasma makes the electron gyrofrequency much larger than the plasma frequency; this substantially modifies the power spectrum for either mode by increasing the Alfven velocity. An estimation of the radiation impedance of bare tethers is also considered. iib) In LJO, a spacecraft orbiting in a slow downward spiral under the radiation belts would allow determining magnetic field structure and atmospheric composition for understanding the formation, evolution, and structure of Jupiter. Additionally, if the cathodic contactor is switched off, a tether floats electrically, allowing e-beam emission that generate auroras. On/off switching produces bias/current pulses and signal emission, which might be used for Jovian plasma diagnostics. In LJO, the ions impacting against the negative-biased tether do produce secondary electrons, which racing down Jupiter’s magnetic field lines, reach the upper atmosphere. The energetic electrons there generate auroral effects. Regions where the tether efficiently should produce secondary electrons are analyzed. iic) Other scientific application suggested in LJO is the in-situ detection of charged grains. Charged grains naturally orbit near Jupiter. High-energy electrons in the Jovian ambient may be modeled by the kappa distribution function. In complex plasma scenarios, where the Jovian high electric field may accelerate charges up superthermal velocities, the use of non-Maxwellian distributions should be considered. In these cases, the distribution tails fit well to a power-law dependence for electrons. Fluctuations of the charged grains for non-Mawellian distribution function are here studied. iii) The present thesis is concluded with the analysis for de-orbiting satellites at end of mission by electrodynamic tethers. A de-orbit tether system must present very small tether-to-satellite mass ratio and small probability of a tether cut by small debris too. The present work shows how to select tape dimensions so as to minimize the product of those two magnitudes. Preliminary results of tape-tether design are here discussed to minimize that function. Results for de-orbiting Cryosat and Envisat are also presented.

The determination of ionospheric charged particle temperatures from in situ measurements

The recently noticed disagreement between ionospheric charged-particle temperature values obtained from ground-based (incoherent backscatter) and in situ (Langmuir probe type) measurements is considered; it is suggested that a main cause of disagreement lies in the poor theoretical basis of present in situ measurements. It is pointed out that the usually neglected geomagnetic field influence may result in too high an electron temperature. It is also shown that the theory used at present to interpret data from ion retarding potential analyzers has serious pitfalls, and that these devices greatly disturb the surrounding plasma when measuring ion temperature. Finally, it is shown how the ion temperature can be accurately obtained from the characteristic of a cylindrical Langmuir probe in a rarefied plasma flow.

On the production of N-2(+) ions at the N 1s edge of the nitrogen molecule

The N+2 ion yield of the N2 molecule has been measured at the N 1s → Rydberg excitations. It displays Fano-type line shapes due to interference between direct outer-valence photoionization and participator decay of the core-excited Rydberg states. The N+2 ion yield is compared with the total intensity of the outer-valence photoelectron lines obtained recently with electron spectroscopy (Kivimäki et al 2012 Phys. Rev. A 86 012516). The increasing difference between the two curves at the higher core-to-Rydberg excitations is most likely due to soft x-ray emission processes that are followed by autoionization. The results also suggest that resonant Auger decay from the core–valence doubly excited states contributes to the N+2 ion yield at the photon energies that are located on both sides of the N 1s ionization limit.

Determination of the hoop fracture properties of unirradiated hydrogen-charged nuclear fuel cladding from ring compression tests

In this work, a new methodology is devised to obtain the fracture properties of nuclear fuel cladding in the hoop direction. The proposed method combines ring compression tests and a finite element method that includes a damage model based on cohesive crack theory, applied to unirradiated hydrogen-charged ZIRLOTM nuclear fuel cladding. Samples with hydrogen concentrations from 0 to 2000 ppm were tested at 20 �C. Agreement between the finite element simulations and the experimental results is excellent in all cases. The parameters of the cohesive crack model are obtained from the simulations, with the fracture energy and fracture toughness being calculated in turn. The evolution of fracture toughness in the hoop direction with the hydrogen concentration (up to 2000 ppm) is reported for the first time for ZIRLOTM cladding. Additionally, the fracture micromechanisms are examined as a function of the hydrogen concentration. In the as-received samples, the micromechanism is the nucleation, growth and coalescence of voids, whereas in the samples with 2000 ppm, a combination of cuasicleavage and plastic deformation, along with secondary microcracking is observed.

Fast ignition driven by quasi-monoenergetic ions: Optimal ion type and reduction of ignition energies with an ion beam array

Fast ignition of inertial fusion targets driven by quasi-monoenergetic ion beams is investigated by means of numerical simulations. Light and intermediate ions such as lithium, carbon, aluminum and vanadium have been considered. Simulations show that the minimum ignition energies of an ideal configuration of compressed Deuterium-Tritium are almost independent on the ion atomic number. However, they are obtained for increasing ion energies, which scale, approximately, as Z2, where Z is the ion atomic number. Assuming that the ion beam can be focused into 10 ?m spots, a new irradiation scheme is proposed to reduce the ignition energies. The combination of intermediate Z ions, such as 5.5 GeV vanadium, and the new irradiation scheme allows a reduction of the number of ions required for ignition by, roughly, three orders of magnitude when compared with the standard proton fast ignition scheme.

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.