Numerical modeling of electron emission from the walls of high-power waveguides* Peter Stoltz Tech-X Corp. collaborators: J. Cary, P. Messmer (Tech-X) V. Dolgashev, S. Tantawi (SLAC) *Work funded by DoE HEP and OFES through SBIR Phase II grant

A brief history of Tech-X Founded in 1994 by S. Shasharina and J. Cary as an SBIR company (90% of funding is SBIR) 19 employees (11 PhD physicists) We focus on computational modeling of charged particles/electromagnetics

Tech-X helps develop a freely-available electromagnetic PIC code called VORPAL VORPAL is a 2D/3D, finite-difference time-domain code VORPAL is owned by Univ. of Colorado and is free for non-commercial and federal research use

Tech-X helps develop a freely-available electromagnetic PIC code called VORPAL VORPAL has: multiple species cold neutral gas resistive walls Child-Langmuir emission VORPAL is getting: secondary electrons neutral gas dynamics impact ionization Fowler-Nordheim emission VORPAL does not have: r-z capability graphical interface

Our simulation geometry of the SLAC high B-field configuration: =11.4 GHz E=80 MV/m 2.3 cm k=196 m-1 0.13 cm 5.0 cm

Single-particle error studies provide a handle on the resolution needed error in vel. down waveguide number of cells along E-field The velocity along the guide is a sensitive measure of code accuracy.

Single-particle error studies provide a handle on the resolution needed The velocity along the guide is a sensitive measure of code accuracy

VORPAL result agrees roughly with semi-analytic result for energy lost to wall Green points are VORPAL results, red are analytic result from integrating E0sin(t+)

VORPAL has space-charge limited emission (Child-Langmuir) density This amount of current ensures zero field at the metal surface But it's really for DC, steady-state And it says nothing about the detailed generation of the electrons velocity

But CL emission alone isn't enough! We use ions to draw enough current To make up the difference, we put ions in the system to partially neutralize the electrons Ions are one solution...field enhancements due to surface structures are another solution

With ion currents, we do see reflection Including ion currents allows a dense enough electron plasma to form so that power is reflected Presently, we add ions in a completely ad hoc manner: ion current starts at specified time

Sandia researchers considered neutral desorption in their ion source experiments Charge exchange is important...ions are accelerated then neutralized, leading to a quickly-expanding neutral gas *Welch, et al, Phys. Plasmas 3 (5), p. 2113 (1996)

Estimate for doing all the scales of this problem says we need implicit solver Cell size: 0.25 um x 25 um x 25 um = 1.56e-16 m-3 Simulation: 1 mm x 2 cm x 4 cm = 8.0e-07 m-3 Number of cells: 2.56e10 Explicit timestep is dt = 0.833fs For 50ns, we would need 6.e7 steps! Conclusion: for these problems, since we can't cheat much more on the spatial size, we need an implicit EM solver (to let us increase the timestep)!