# Theory of a Helical Resonator Plasma Source

### Michael A. Lieberman, Allan J. Lichtenberg and D.L. Flamm

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M90/10

1990

A helical resonator plasma source is a resonant, slow wave, plasma-loaded structure consisting of a cylindrical plasma surrounded by a helical coil which, in turn, is surrounded by a grounded coaxial cylinder. Such sources can be efficiently matched to an external power source and can operate at low gas pressures. We employ a developed sheath helix model, in which the cylindrical geometry is unfolded into a rectangular geometry and the RF current in the helix wires is replaced by a continuous current sheet, to obtain the dispersion characteristics (Beta versus omega, where Beta is the axial wavenumber and omega is the frequency) for the slow waves, their electric and magnetic fields, and the scaling of the dispersion and fields with source parameters and geometry. We use a quasistatic approximation to obtain the fields in a cylindrical structure and including plasma collisions. These results are then used to calculate the stochastic heating, which dominates at low pressures, and the ohmic heating, which dominates at high pressures. We determine the resulting plasma density, loaded resonator Q, and source coupling. The theory is compared to some preliminary experimental results.

BibTeX citation:

@techreport{Lieberman:M90/10, Author = {Lieberman, Michael A. and Lichtenberg, Allan J. and Flamm, D.L.}, Title = {Theory of a Helical Resonator Plasma Source}, Institution = {EECS Department, University of California, Berkeley}, Year = {1990}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/1408.html}, Number = {UCB/ERL M90/10}, Abstract = {A helical resonator plasma source is a resonant, slow wave, plasma-loaded structure consisting of a cylindrical plasma surrounded by a helical coil which, in turn, is surrounded by a grounded coaxial cylinder. Such sources can be efficiently matched to an external power source and can operate at low gas pressures. We employ a developed sheath helix model, in which the cylindrical geometry is unfolded into a rectangular geometry and the RF current in the helix wires is replaced by a continuous current sheet, to obtain the dispersion characteristics (Beta versus omega, where Beta is the axial wavenumber and omega is the frequency) for the slow waves, their electric and magnetic fields, and the scaling of the dispersion and fields with source parameters and geometry. We use a quasistatic approximation to obtain the fields in a cylindrical structure and including plasma collisions. These results are then used to calculate the stochastic heating, which dominates at low pressures, and the ohmic heating, which dominates at high pressures. We determine the resulting plasma density, loaded resonator Q, and source coupling. The theory is compared to some preliminary experimental results.} }

EndNote citation:

%0 Report %A Lieberman, Michael A. %A Lichtenberg, Allan J. %A Flamm, D.L. %T Theory of a Helical Resonator Plasma Source %I EECS Department, University of California, Berkeley %D 1990 %@ UCB/ERL M90/10 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/1408.html %F Lieberman:M90/10