Sheath parameters for non-Debye plasmas: Simulations and arc damage

Abstract

This paper describes the surface environment of the dense plasma arcs that damage rf accelerators, tokamaks, and other high gradient structures. We simulate the dense, nonideal plasma sheath near a metallic surface using molecular dynamics (MD) to evaluate sheaths in the non-Debye region for high density, low temperature plasmas. We use direct two-component MD simulations where the interactions between all electrons and ions are computed explicitly. We find that the non-Debye sheath can be extrapolated from the Debye sheath parameters with small corrections. We find that these parameters are roughly consistent with previous particle-in-cell code estimates, pointing to densities in the range 10 24 -10 25 m À3 . The high surface fields implied by these results could produce field emission that would short the sheath and cause an instability in the time evolution of the arc, and this mechanism could limit the maximum density and surface field in the arc. These results also provide a way of understanding how the properties of the arc depend on the properties (sublimation energy, for example) of the metal. Using these results, and equating surface tension and plasma pressure, it is possible to infer a range of plasma densities and sheath potentials from scanning electron microscope images of arc damage. We find that the high density plasma these results imply and the level of plasma pressure they would produce is consistent with arc damage on a scale 100 nm or less, in examples where the liquid metal would cool before this structure would be lost. We find that the submicron component of arc damage, the burn voltage, and fluctuations in the visible light production of arcs may be the most direct indicators of the parameters of the dense plasma arc, and the most useful diagnostics of the mechanisms limiting gradients in accelerators.

An integrated approach to understanding RF vacuum arcs

“…Particle in cell, (PIC) codes show that the initial plasma temperature, both and is cool, only a few eV, however the sheath potential between the plasma and the walls can be significantly higher than the plasma temperature. This relationship persists as the density increases and the system eventually becomes non-Debye 36 . Data on arc damage shows the arcs are roughly 500 m in diameter 9 .…”

“…Self-sputtering from plasma ions and sublimation maintains the ion density 33 , Image charges provide the charge to stick the plasma to the surface. And the density rises until the plasma plasma becomes non-linear (non-Debye) 36 .…”

“…3.48 in Anders 1 and Anders et al 35 . The arc properties are strongly dependent on the plasma sheath 34 , 36 , 37 , particularly ion self sputtering at high temperatures and high tensile stresses. When combined with other existing data on arc behavior, modeling using PIC and Molecular Dynamics (MD) codes, see Fig.…”

Computational problems in modeling arcs

“…Computational limitations imply timesteps for these calculations on the order of 10 -18 -10 -17 s and equilibrium times of 10 -13 s, over geometrical dimensions of 10 -9 m, many orders of magnitude smaller than the dimensions of PIC calculations 6 . On the other hand, MD calculations can be used when the densities are high enough so that the total electrostatic energy of the system is comparable to the kinetic energy of the particles (the nonideality parameter, Γ = electrostatic/kinetic energy ~0.5) 6 . MD calculations are not, in principle, compatible with PIC calculations, thus we use them to define boundary conditions and evaluate sputtering coefficients rather than to describe the evolution of the system as a whole…”

“…With a basic knowledge of the scale of parameters like the Debye length, sheath potential and field emission, it is possible to generate explanations for self quenching of unipolar arcs, and other phenomena 6 . Likewise, studies of the cooling of thin liquid surfaces can begin to explain the range of surface damage seen in arcing.…”