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Plasma Heating by Intense Charged Particle-Beams Injected on Solid Targets T PLASMA HEATING BY INTENSE CHARGED PARTICLE-BEAMS INJECTED ON SOLID TARGETS T. Okada, T. Shimojo, K. Niu To cite this version: T. Okada, T. Shimojo, K. Niu. PLASMA HEATING BY INTENSE CHARGED PARTICLE-BEAMS INJECTED ON SOLID TARGETS. Journal de Physique Colloques, 1988, 49 (C7), pp.C7-185-C7-189. 10.1051/jphyscol:1988721. jpa-00228205 HAL Id: jpa-00228205 https://hal.archives-ouvertes.fr/jpa-00228205 Submitted on 1 Jan 1988 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C7, supplgment au n012, Tome 49, dbcembre 1988 PLASMA HEATING BY INTENSE CHARGED PARTICLE-BEAMS INJECTED ON SOLID TARGETS T. OKADA, T. SHIMOJO* and K. NIU* ' Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei-shi, Tokyo 184, Japan *~epartmentof Physics, Tokyo Gakugei University, Koganei-shi, Tokyo 184, Japan Department of Energy Sciences, Tokyo Institute of Technology, Midori-ku, Yokohama 227, Japan Rbsunb - La production et le chauffage du plasma sont estimbs numbriquement B l'aide d'un modele simple pour l'interaction de faisceaux intenses d'blectrons ou protons avec plusieurs cibles solides. On obtient ainsi les longueurs d'ionisation et la temperature du plasma produit. Abstract - The plasma productions and subsequent heatings of the plasmas are calculated numerically by a simple model when intense charged-particle beams composed of electrons or protons are impinged on several solid targets. The ionization lengths and plasma temperature ara obtained. 1 - INTRODUCTION It is the one of the most important problems to investigate interactions of charged particle with solid-targets for inertial confinement fusion. Especially, the quantities such as ioniza- tion length and temperature of the 'produced plasma on the surface of a solid target must be in- vestagated for the design of the most suitable targets. There has been many investigations 11-31 of the mechanism of production and heating of the plasma on the surface of a solid. The plasma produced by charged particle-beams blows out outward and the density gradient is formed on the surface of the target. The density changes from about lx10~?-cm-~in the solid-density region, through 1x10~9cm-3 in the intermidiate region, to below 1x1015 cm-3 in the rarefied region 141. Thus the phenomena is divided into two stages; In the first stage, the production of plasma from a solid-target and heating of it are considered before blowing out of the produc- ed plasma. In the second stage, the heating of blow-out plasma is considered /3,5/. The former stage is that at the beginning of injection of beams of some durations. The ion temperature of the plasma is thought to be too low in this stage to permit the blow-out of the plasma after ionization. In this stage, the density of the plasma remains to that of solid. Then the physics which govern this stage will mainly be ionizatioq, bremsstrahlung, and close and far collisior~s. The heating of the produced plasma by the charged particle beam is due to the close and far collisions in this stage. In this paper, we confine ourselves to the study-of the production of plasma and subsequent heating of it in the solid-density region in the first stage and compare the results of'the cases of electron and ion beams. 2 - ENERGY LOSSES OF A CHARGED PARTICLES The kinetic energy of a charged particle in an injected beam is converted into ionization energy of a solid target, thermal energy of the produced plasma and radiation energy. The energy losses of a charged particle are calculated from: wnere E is the kinetic energy of the incident particle and x is the distance from the target surface along the direction of the beam propagation. The F corresponds to energy loss due to ionization (inelastic collision), F the one due to close and1 far collisions, and F due to 2 3 brmsstrahlung. The force F2 is mainly responsible for the plasma heating. In the numerical crlculation the following assumptions are made; (i) The radius of the beam does not change in the target. (i;) The atoms of the target are ionized singly or highly by the beam-particle and also by the plasma-particles. We assume here, however, that the atoms of the target are ionized singly by the beam-paraticles in all the regions of time and space for simplicity. (Lii)The avalanche process by secondary electron is neglected. (-v) The ionization process in a part of the target continues till all the atoms in the part are ionized singly, that is, till fully-ionized plasma is produced. (J) The radiation loss of the beam-particle is taken into account for electron-beams, but neglected for iorl-beams. A~iu dso, che rndiatiolr iosb or the prouucud plisma is neklected, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988721 C7-186 JOURNAL DE PHYSIQUE (vi) The radiation emitted by the beam-particles is not re-absorbed by the plasma. (vii)The energy deposited by the charged particle-beam through close and far collisions is con- verted to the thermal energy of plasma particles instantaneously. (viii)The effect of thermal conduction in the plasma is neglected completely. (I) The case of electron beams For this case, the force F1 is given 161 by where N is the number density of target atoms, Z the atomic number of them, u the electron rest energy, z the charge number of beam-particles, 6 equal to v/c (v: the speet of beam-particle, c: the speet of light), I the average ionization energy of the target atom divided by Z, W the maximum energy given from beam particle to free electron Wm= E/2 and $0= 8nr6/3. Here ro ?s the classical radius of electron ro = e2/mOc2, where -e and mo represent the charge and the rest mass of electron, respectively. The force F is given in /7/ by 2 where wpe is the electron plasma frequency, h is the Plank constant divided by 2a, and mb and m stand for the mass of beam-particle (electron) and plasma-electron with relativistic correc- tions, respectively. Expression (3) can be used in the quanta1 case, where the condition v 2 vc = ze2/fi = 2.2~10~crn.sec-~holds for the beam-particle of z=1, and the exchange effect is included in this expression. The speed of a beam-particle decreases from the initial value VbO = (2~/m) to the thermal speed vzh= (3~~/m)~/~of the plasma-electrons. Here V and Te are the initial values of the kinetic energy and the electron temperature of the plasma, respectively. We assume that the initial values of temperatures of both electrons and ions in the produced plasma are equal to 1.0 eV. In this case, vEhz vC, and the inequality v 2 vc holds, when V is in the range between 1 KeV and 1 MeV. Then the use of the expression (3) is reasonable in the nu- merical calculations. The radiation losses are also important for electron-beams with high energies over 1 MeV. The force F which corresponds to bremsstrahlung loss is given in by 3 /8/ where $ =I6313 and $=~~ri/137.As the force F3 includes the factor z2, the radiation losses become fzgortant for targets with large values of Z. The comparisons of the magnitudes of El, F2 and F3 vs 6 for each material of target for the case of electron beams are shown in Figs. 1-3. (11) The case of proton beams For a light ion beam as proton, we can use following expression for F 1161: For proton, vbo becomes 4.3~10~cm.sec-~or 2.0~10~cm.sec-~when V=100 KeV or 2 MeV, respectively, and vEh 2 1.2xl0~cm.sec-~ for a plasma of which electron temperature is above 1 eV. As the beam particles slow down from vbo to vth, the force F2 must be changed from ~$9)in the region of velocity v t vr to F2(~) of classical case in vr t v 2 vgh, where vl is set to vc/10 in this paper and vy : 2.2xl0~cm.sec-~ for proton. The forces F2(q) and F~(c) are given in /8/ by and 2 4 2rnrnbV3 (1 [ F2 mv yze (m + %)wpe I, respectively, where yz1.78107. As the proton beam with kinetic energy of several MeV is non-relativistic, the radiation losses by the beam-particles can be neglected cdmpletely. The comparisons of F1, ~~(9)and F~(c) are shown in Figs. 4-6 for several materials of targets for the case of proton-beams. Fig. 1 - F1, F2 and F3 vs B=v/c of an elect- Fig. 2 - F1, F2 and F3 vs $ of an electron ron for solid D2 target. The abscissa stands for polyethylene target. The hydrogen atoms for 6, and the ordinate does F1 and F2 (left are replaced by deuteron atoms. Double peaks hand side) and F3 (right hand side). in F1 comes from the fact that polyethylene target is composed of D and C. Fig.
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