Basko EPS2006 iac

Category: Entertainment

Presentation Description

No description available.


Presentation Transcript


Test ion acceleration in the field of expanding planar electron cloud M. M. Basko Institute for Theoretical and Experimental Physics, Moscow 33rd EPS Conference on Plasma Physics Rome, Italy, 19-23 June 2006


Question: how to calculate the maximum energy of an accelerated test ion? The usual approach, based on using the Boltzmann relation Motivation turns out to be inadequate because it leads to a diverging answer the true value of the “diverging” logarithmic factor depends on how accurately the Botlzmann-Maxwell distribution is established in its far tail, for which there simply may be not enough time after the laser pulse. Conclusion: in general, the Boltzmann relation cannot be used to solve our problem.


Formulation of the problem At time t=0 all electrons ― treated as a collisionless charged fluid ― of a uniform planar foil are accelerated to the same velocity v0. The main foil ions are assumed to be infinitely heavy and staying at rest. A test ion of charge +eZp and mass mp begins to accelerate at t=0 from its initial position x=0 at the foil surface. Questions: Can a test ion reach the electron velocity v0 ? Earlier this problem was considered by Bulanov et al. (Pl. Phys. Rep., 30, p.18, 2004); here we correct and expand the results of their work. Can it overtake the electron front ?


Principal parameters and variables There are three independent dimensionless parameters which govern our problem Principal unknown variables:


Electron trajectories xe(t,) Analytical results are most readily obtained for =0 (l0  0, n0l0 = finite).


Electron cloud structure Asymptotically, the relaxation zone expands linearly in time, with 0 = 0.250.02 for =0, 0=1. In the quasi-equilibrium core of the relaxation zone one can use the Boltzmann relation. In the laminar zone the present solution applies.


Motion of test ions (general features) Motion of a test ion can be analyzed analytically only in two cases: the ion trajectory lies entirely in the laminar zone; the ion trajectory lies entirely in the quasi-equilibrium core, where the hot electrons obey the Boltzmann relation. Our new exact results are exclusively for test ions accelerated in the laminar zone !  They apply within a limited domain of the , , 0 parametric space.


Ion equations of motion Dimensionless equations of motion (=0): Transformation to new “hyperbolic” variables: Phase equation: Integral trajectories in the , phase plane


Maximum energy of a test ion only sufficiently light test ions with  > cr can catch up with the electron front and overtake it; Main results: for each value of 0 there exists a critical value cr=mcr(g0) of parameter  = Zpme/mp such that Alternatively, for each value of m there exists a critical value of g0 = gcr(m) such that a test ion with mass ratio m overtakes the electron front when g0 > gcr(m) . heavier test ions with  < cr lag behind the electron front, and only asymptotically, on a time scale ~exp(0.5 -1), approach the electron velocity v0;


Acceleration of test ions by ultra-relativistic electrons Only for highly ultra-relativistic electrons with 0 >> 1000 does the critical charge-over-mass ratio cr begin to drop significantly below 1/8 !


Practical implications Acceleration of protons: protons can overtake the electron front only when 0 > 0.5 exp(1827.5) = 2·10793 ― which is beyond any realistic value ! for 0 -1 << 1 the proton trajectory lies inside the equilibrium Boltzmann zone: Target example: 1μm of gold (ionization z=50, ne=3x1023 cm-3), 0=100   = 10. for 0 > 348 ( = 0) → 537 ( > 3) the proton trajectory lies inside the laminar zone;


Conclusions In practice, protons and heavier test ions can never catch up with the electron front. If hot electrons are non-relativistic or moderately relativistic, acceleration of test ions in the non-equilibrium laminar zone near the electron front is relatively inefficient; the situation is close to the Boltzmann equilibrium. For highly relativistic electrons (0 > 300) the non-equilibrium structure of the expanding electron cloud becomes important. In the planar geometry, the maximum ion energy depends logarithmically either on elapsed time, or on the traveled distance.

authorStream Live Help