Interaction of heavy-ion beams with target plasma Ryouji Takahashi, Toshihiko Hotta, and Toshio Okada Citation: AIP Conference Proceedings 369, 1138 (1996); View online: https://doi.org/10.1063/1.50399 View Table of Contents: http://aip.scitation.org/toc/apc/369/1 Published by the American Institute of Physics Interaction of Heavy-Ion Beams with Target Plasma Ryouji Takahashi, Toshihiko Hotta, Toshio Okada Faculty of Technology, Tokyo University of Agriculture and Technology, 2-24-16 Naka- machi, Koganei-shi, Tokyo 184. Abstract. Heavy-ion beams have been considered as a driver for inertial confinement fusion. The interaction of the ion beam with a target plasma is of central importance. A number of studies on the heavy-ion beam interaction with target plasma are found in the literature 1-4. Reported are the results of a numerical study of an effective charge and nonlinear corrections to the stopping power for heavy ions in plasma. It is important for heavy-ion stopping that charge states of projectile ions are decided. The effective charge states of beam ions are supposed as Betz formula. It is shown that the stopping power is increased and the stopping range is shortened according to nonlinear effects. The heavy-ion stopping is simulated at the various temperatures of the target plasma. The target heating of the ion beam and radiation effects are investigated.Energy is decreasing by the varying of the electric and magnetic fields in the target. It is considered to be a collective effect of stopping power. Though it is very small, in fact, there is the energy loss. Here it is shown that by using the PIC code. Effective charge theory One t e r m that we have not satisfactorily defined thus far for use in the Bethe model is Zeff, is the effective charge of the projectile ion. T h e effective charge of an ion is usually inferred by comparing the stopping power of a higher-Z ion to t h a t of a proton. Any deviation from a Z 2 dependence is attributed to an effective charge. Betz, Brown, Moak, Steward, and Ziegler have published "least-squares fits" to the effective charge. We have found that the concise expression given by Brown and Moak (Eq.(1)) contributes to a good agreement between computed and experimental stopping powers when used in conjunction with our set of average ionization potentials and shell corrections. Zeff = Z0(1 -- 1.034exp(-137.04~/(Zo)°'ng)) (I) © 1996AmericanInstituteof Physics 1138 where Zeff is effective charge, Z0 atomic number, 13=Vp/c, Vp is ion velocity and c light velocity. Linear Vlasov theory The Vlasov-Poisson equations without external fields read Of + v . Of + 0¢~ . -Of- = 0 . o~ ~ 0~ The electrostatic potential is given by (I)l(r,t) = Zeff Jf (2) Ov 3 exp(ik. (r - Vpt)) k k2~(k, k • Vp) (3) I The Linear stopping power is calculated by using asymptotic expansion - where Z = 3Z~' (4) in Nm = no~3D, no is the density of plasma ~D Deby length. Nonlinear Vlasov theory During the collision, the election will be displaced by ~ due to the force of the ion: ~ + w2~ = f/m, where f(t,b) is the force by the ion. The equation of motion can be rewritten the form ¢(t) 1 tt I - TruMp J-z~ dtf(t, b) sin[wp(t - [)] (5) with the force F(t,b) = z ~ff e~ (v~t + ~)ex + (b + %)% [(-~vt + ¢x)2 + (b + ~u)213/2' (6) The energy transfer is 2 1 dtF(t, b) exp(iwpt) . (7) Nonlinear stopping power is calculated by using the Bessel function and the Bark.s term - ~ - 2~v~= In IZI + ~ 1139 in IZl - 2.4 . (8) Particle-in-cell simulations At first, by determining the distribution of particles and the initial ion velocity, electric and magnetic fields are calculated by Maxwell equations. VxE(x,t) V × E(x,t) eoV.E(x,t) V.B(x,t) = : = = -°B(x,t) #0(e0°E(x,t) +j(x,t)) p(x,t) 0 (9) The particle motion and electric and magnetic fields are calculated by using Eq.(9) and difference methods. Thus the energy loss of the projectile particle is determined. Where numerical value is using the normalization. The normalization unit is shown in table 1. Initial conditions are shown in table 2. Table 1: Normalization units space c/~op velocity c time dencity no mass me charge q current 47rnoqc electric field (47mom~ca)1/2 magnetic field (47rnom~c2)l/2 no(c/wp)Zmc2/2 energy Table 2: Initial conditions heavy-ion beam species Bi atmic number 83 continue time 10[ns] beam density 3.0 × 1015[cm-~]"'' energy of one particle 30[MeV] target species Li atomic number 3 1.0 x lO~2[cm-3] plasma density plasma temperature lO00[eVl 1140 ISOIXI I . . . . I ' ' ' I ' },= ct~ 0~-I 0 5xlO "i IxlO -~ i ~ 0 Fig.1 The linear and nonlinear calcuIation ['or stopping power with constant temeprature T=1000(eV]. The solid line, numerical evaluation of the linear stopping power Eq.(4); dashed line, numerical evaluation of the nonlinear stopping power Eq.(8). . , , . , . . [ i 5 ~10-1 Distance (cm) Distance (cm) E r r l x l 0 -~ Fig.2 The solid line is the result of the effective charge by taking the [inear stopping power.The dashed line is the result of the effective charge by taking nonlinear stopping power. , ~88.6 I3424 ~ 238&~ M 13423 2~$8.2 c~ 13422 2388 [ ] 200 Time t ~ i I 1 [ r 0.00 Time (1/co p) Pig.3 The stopping power by PIC code. Energy loss is normalized. (1/co p) Fig.4 The stopping power by PIG code. Energy loss is not normalized. 1141 L-i Discussion In summary, we have calculated HIB stopping power in consideration of the nonlinear and collective effects. According to Fig.l, it is shown that the stopping power is increased and the stopping range is shortened according to nonlinear effects. According to Fig.3, there is the energy loss by collective stopping power, but it is shown that energy loss of the collective stopping power is not too large. References 1. 2. 3. 4. E.Nardi, E.Peleg and Z.Zinamon, Phy. E.Nardi, Z.Zinamon, Phys. Rev. Lett. Th.Peter and J.Meyer-ter-Vehn, Phys. Th.Peter and JMeyer-ter-Vehn, Phys. Fluids 21, 574 (1978). 49, 1251 (1982). Rev. A43, 1998 (1991). Rev. A43, 2015 (1991). 1142

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