1. 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

2. 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

3. 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

4. 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

5. 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

6. 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.

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

8. 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+)

9. 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

10. 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

11. 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

12. 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 (1996)

13. 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)!