A method for obtaining three-dimensional computation equilibrium of non-neutral plasmas using WARP Page: 4 of 34
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shown in Fig. 1. In an actual experimental trap, electrons are injected from a negatively
biased cathode, enter the confinement region, and reflect from the negative potential at
the far end of the trap.
The plasma is created when electrons are trapped as the voltage is changed on a
nearby gate. The electrons enter the system with energies of a few eV and, if the walls are
cold, may subsequently cool (via synchrotron radiation) to the wall temperature. In a
simulation, a method based on first principles would require simulation of the injection
from the cathode, and the subsequent approach to equilibrium via synchrotron cooling.
However, such an approach appears to be impractical on current computers (even
supercomputers) using standard simulation methods, if the actual processes and their
associated time scales are to be captured accurately. In a similar approach (but without
synchrotron cooling), phase-mixing arising due to the numerical collisions in a PIC code,
would eventually drive the trapped plasma to an equilibrium; however, the characteristics
of such an equilibrium may might differ substantially from those of the one equilibrium
that is reached experimentally.
An alternative is to start the simulation either from an arbitrary plasma distribution or
from a prescribed idealized equilibrium state. We have performed studies of the evolution
of distributions with an initial Gaussian longitudinal velocity distributions, and with a
variety of (arbitrary) plasma densities. These studies show that the plasma evolves, via
halo formation, to phase-mixed equilibrium that are, as described in Appendix B, near to
the corresponding idealized distribution. However, even a straightforward loading of an
idealized equilibrium does not, unfortunately, correspond to a computational equilibrium.
and the distribution may distort, becoming noisy and deviating from the original
equilibrium. Without special coding, realistic collisions are not present in a PIC code.
Furthermore, it is not clear, even if one were to successfully obtain a computational
equilibrium, that this equilibrium would be maintained when parameters of the system
are slowly varied.
Nonetheless, it is important to obtain a tool that enables computing the equilibrium in
the trap of the non-neutral plasma with specific electrostatic and magnetic fields at a
definite temperature, especially if the analytical specification of the equilibrium
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Wurtele, J.; Wurtele, J.; Friedman, A.; Grote, D.P.; Vay, J-L. & Gomberoff, K. A method for obtaining three-dimensional computation equilibrium of non-neutral plasmas using WARP, article, March 25, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897957/m1/4/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.