Resistive wall instability in a uniform beam: simulation vs analytical results Page: 4 of 27
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The Resistive Wall Instability in a Uniform Beam:
Simulation vs. Analytical Results
Lawrence Berkeley Laboratory
University of California
Berkeley, California 94720
The time-dependent behavior of the resistive wall instability in a uniform
charged beam is investigated by means of computer simulation. Results are
compared with linear analytical results for a range of cases in which two
parameters are varied: the resistive wall term and the initial thermal spread
of the beam. In general we find good agreement between simulation and
theoretical results. The main conclusion is that the growth rate of any mode
increases with the resistive term and decreases as a function of the thermal
spread. There is always a maximum marginally unstable wavenumber k for any
nonzero thermal spread. The linear growth rate is roughly the same for the
thermal spread and for the electric field amplitude. An "overshoot"
phenomenon is present, in the sense that the thermal spread continues to grow
after the electric field has reached saturation.
A cold uniform beam with space-charge is unstable against perturbations if
a resistive wall force is present. However, a non-zero thermal spread in the
beam has a stabilizing effect, quenching the growth of all wavelengths shorter
than a certain limiting value. This limiting wavelength (or correspondingly,
wavenumber) is a function of: (a) R'-wall resistance per unit length, (b)
vth-thermal spread, (c) other physical parameters like: vB-the beam
velocity, n-number of particles per unit length, q-charge per particle, m-mass
of particle, g-geometric factor related to pipe and beam radii.
It is the purpose of this report to study the above phenomena by means of
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Sternlieb, A. Resistive wall instability in a uniform beam: simulation vs analytical results, report, June 1, 1981; California. (https://digital.library.unt.edu/ark:/67531/metadc1203428/m1/4/: accessed March 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.