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

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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 ionization 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 produced 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,

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(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 converted 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 numerical 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. 3 - Fl, F2 and F3 vs 6 of an electron Fig. 4 - F1 and F2 vs $ of a proton for solid for Au target. Fl is obtained in the range D2 target. 820.6. When $<0.6, the electron beam can not ionize the Au atoms. JOURNAL DE PHYSIQUE

Fig. 5 - F1 and F2 vs B of a proton for poly- Fig. 6 - Fl and F2 vs B of a proton for Au ethylene target. target. For B50.3, ionizations do not occur. 3 - RESULTS OF NUMERICAL CALCULATIONS The ionization lengthes and the average temperatures of electron and ion are shown in Figs.7-12 for targets of solid D2, polyethylene and gold as the functions of the kinetic energies V of electron and proton beams for the case of two values of energy fluxes, i.e., ~=1.0x10~~and ~=1.0x10~~joule.sec-~.cm-~.The number density of the solid D2 target is put equal to 5.0x10~~cm-3. For polyethylene target in which the hydrogen atoms are replaced by the deuteron atoms, the number density of D is 1.7x10~~cm-3and that of C is 8.6x10~~cm-~.For Au target, N=5.9~10~~cm-3. General feature of the results is as follows; The ionization length XFIN is independent of the value of the energy flux. As the initial velocity vbo of the beam particle increases, the length becomes large. As a result, average temperatures T~Vand T~Vdecrease since beam energy is expended to ionize large number of atoms in the target. The length XFIN becomes shorter as the value of Z increases at the fixed initial energy of the beam particle and the fixed energy flux of the beam. For most cases, the ionization length X reaches to XFIN in several nano-seconds which is shorter than the beam duration ~=4.0x10-~sec. The number of ionization layers increases in general when the atomic number Z of the target atoms becomes large at the same incident kinetic energy of the beam particle. Energy layer has different temperature, and temperature gradient is formed in a target, which changes with time. Since the thermal conduction is neglected in this model, it is meaningless to check precisely the gradient. Then the average electron and ion temperature at the time t=r are shown in the figures in this section. In all Fi s 7-12, solid lines and dashed lines represent the results for ~=1.0x10~~and 1.0x1014Joule.sec-f~~m-2, respectively. (I) The case of electron beams (i) Solid D2 target. Only one ionization layer is formed when vb0~2x10~cm.sec-1and beam particles slow down to v:h in the layer. When VQl MeV, the XFIN reaches about 3cm. Then electron beam can pass through the bare target of solid D2 if the thickness of the latter is smaller than 3cm. The results of calculations re shown in Fig. 7. (ii) Polyethylene target. The XFIN on polyethylene target are smaller than those on solid D2 target by one order of magnitude. Fig. 8 shows the results of calculations. (iii) Au target. The main feature is that the bremsstrahlung loss of electron beam is very large compared to that in other targets of low Z materials. Fig. 9 shows the results of calculations. As it is clear from Fig. 3, F1 is much larger than F2 for 8'0.7, then the beam particles are decerelated due to mainly ionization loss and bremsstrahlung loss. Many ionization layers are formed and the plasma are not heated dominantly. (11) The case of proton beams In the case of proton beams, the contribution to the stopping power due to heating losses F2 comes mainly from not plasma ions but plasma electrons. Then it is assumed that initially electron component of the plasma is heated by the proton beam in a region, and afer that electron and temperature relaxation.occurs. That is, force F2 of beam particle is put equal to zero when proton slows down to vth from vbo in a region. The XFIN is smaller about 2 order than that of electron beams for the same incident kinetic energy of the beams injected on the same targets. This difference comes from the fact that the speed of the beam particle is different'with each other for electron and ion beams even they have the same incident kinetic energy. On the contrary to the case of electron beam, the average electron temperature (thermal energy) Tiv can generally be larger than the incident kinetic energy of the beam-proton, although the inequality T~V>T~holds. In the case of proton beams, we assume that the beam particles lose their energy due to F2 until they slow down to not vfh but vth which is the thermal velocity of the plasma ions. (i) Solid D2 target. Only one ionization layer is formed for the incident kinetic energy of the beam in the range from 100 KeV to 1 MeV. Fig.10 shows the results of calculations. (ii) Polyethylene target. The average ion temperatures at t=~stay in almost same values in order over the whole range of incident kinetic energy of the beam, notwithstanding of the difference in the value of beam fluxes. Fig.11 shows the results of calculations. (iii) Au target. Since Au atoms cannot be ionized by the proton beams of V<700 KeV, calculations are performed in the range V2700 KeV. The XF~~at ~=1.0x10~~joule.sec-~.cm-~ are smaller than that at ~=1.0x10~~joule.sec-l. cm-*, since proton beams heat the plasma much effectively in the former case compared to the latter case, and lose the ability of ionizing atom more fastly. The results of calculations are shown in Fig.12. 4 - DISCUSSIONS We confine ourselves to the region of the kinetic energy of the charged particle beam from lOOKeV to 1 MeV, considering the experiments using diodes. However, in the cases of experiments using beams of kinetic energies much higher than several MeV, some problems discarded in this paper will appear. If the targets of high Z materials as gold are bombarded by such relativistic electron beams, the generations of characteristic X-ray by excitations of innershell electrons will be appreciable. Since a beam electron loses large amount of energy by the excitation, the straggling of the beam must be considered, and the ionization length will be shorten as a whole by the process. For proton beams of high velocities, the process of direct nuclear reactions becomes appreciable in addition to the process mentioned above. The criterion for the neglect of such reactions is obtained from the comparison of the total cross sections for ionization, close and far collisions, and bremsstrahlung at a temperature with the cross sections of nuclear reactions. When the charged particle beams are intense, the energy density of the induced electric field becomes large and the state of the plasma changes to a turbulent state. The stopping power of a turbulent plasma for an impinged charge particle is different from that of quiescent plasma. So, there is a possibility of enhancement of energy deposition of the beam particle in the turbulent plasma. The enhancement, in turn, leads to the production of high temperature plasma. In such a plasma, the stopping power will be changed 151. The energy deposition can also be enhanced by the self-magnetic field of a relativistic electron beam under the assumption that the field can permeate into the plasma 191. The magnitude of the self-magnetic field is, however decided from the detail analysis of the propagation and pinching of the electron beams. Such a detail analysis for ion beams are remained for future investigations.

Fig. 7 Fig. 8 Fig. 7, 8 - XFIN (right hand side of the ordinate), T~Vand T~V(left hand side of the ordinate) vs incident kinetic energy V of electron beams (abscissa) at t=4.0x10-8sec (a) and 2.0x10-~sec (b). Solid lines stands for the T~Vor Tiv for ~=1.0x10~~joule.sec-~cm-~and dashed lines for ~=1.0x10~~joule.sec-~.cm~~(Fig. 7 is for solid D2 target and Fig. 8 is for polyethylene target). JOURNAL DE PHYSIQUE

Fig. 9 - Ionization length X, TZv and Tiv vs Fig. 10 - XFIN, Tiv and Tiv vs V of proton time t in Au target bombarded by electron beams for solid D2 target at t=r. beam until t%~xlo-~sec.The length X satu- rates at t%2~10-~sec. V=l MeV and ~=1.0x10~~joule.sec-l.~m-~. x (cm)

It,,. I,," (eV1 X(Em1

Fig. 11 - XFIN, TiV and TB" vs V of proton Fig. 12 - XFIN, TZV and ~i~vs V of proton beams for polyethylene targets at t=r. beams for Au targets at t=r. Ionizations do not occur for VS700 KeV.

REFERENCES

111 Mosher, D., Phys. Fluids 18 (1975) 846. 121 Nardi, E., Peleg, E. and Zinamon, 2, Phys. Fluids 1(1978) 574. 131 Rogerson, J.E., Clark, R.W. and Davis, J., Phys. Rev. A 2 (1985) 3323. 141 Caldirora, P. and Knoepfel, H., Physics of High Energy Density (Academic, New York, 1971). 151 Zinamon, Z. and Nardi, E., Proc. of the 6th Int. Conf. on High-Power Particle Beams (Kobe, 1986) 345. 161 Heitler, W., Quantum Theory of Radiation (Oxford, 1954) Chap. 25. /7/ Seitenko, A.G., Electromagnetic Fluctuations in Plasma (Academic, New York, 1967) Chap. 8. 181 Heitler, W., Quantum Theory of Radiation (Oxford, 1954) Chap. 37. 191 Mosher, D. and Bernstein, I.B., Phys. Rev. Lett. 3 (1977) 1483.