Relaxation of electron and ion temperatures. [(a)–(c)] Evolution in time of the transverse and longitudinal components of the electron mean temperature, and of the ion mean temperatures [(b) and (c)], for (a), (b), and (c). (d) Variation of the electron isotropization time and of the electron-ion thermal equilibration time , as a function of the collision frequency.
Maxwellianization of the electron distribution function. Main panel, distribution functions of the velocity in the expansion direction , for (collisionless plasma) and . These distributions are taken at the center of the foil , when . The dotted line is the Maxwellian distribution function expected for . Inset, spatial variation of the local electron temperature, averaged over twenty meshes, with or without collisions.
Identification of the Maxwellian-isotropic regime of expansion. (a) Dependence on time of the ion front velocity, for collision frequencies . (b) Comparisons of the ion front velocities calculated using the hybrid code or the PIC code. The two curves associated with the hybrid code, labeled “hybrid 1D” and “hybrid 3D” correspond, respectively, to the 1D version of the code described in Ref. 12, and to the isotropic version presented in Sec. III A. The longitudinal temperature is the same in both cases.
Time dependence of the electron mean temperature in the collisionless and isotropic regimes. Solid lines correspond to the PIC code, dashed lines to the hybrid model and dotted lines to the asymptotes and . The result of a PIC simulation including all Coulomb collisions is also plotted (dash-dotted line).
Ion front velocity as a function of time, with or without electron-ion and ion-ion collisions.
Adiabatic expansion of a plasma foil, for . (a) Ion velocity as a function of the distance to the initial position of the plasma surface . The solid line corresponds to the PIC code, the dashed line to the adiabatic self-similar model and the dotted line to the isotherm self-similar model. (b) Ion density, and electron/ion temperatures raised to the power 3/2, as a function of . The temperatures are averaged over twenty meshes. In the adiabatic part of the plasma .
Limit of the adiabatic region as a function of time, for . The value of extracted from the PIC code is the coordinate of the point where . The fit corresponds to the function with .
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