ICAP 2002 Abstracts and Posters
Efficiency of a Boris integrator with spatial stepping
Abstract
A modified Boris-like integration, in which the spatial
coordinate is the independent variable, is derived. This
spatial-Boris integration method is useful for beam
simulations,
in which the independent variable is often the distance
along
the beam. The new integration method is second-order
accurate,
requires only one force calculation per particle per step,
and preserves conserved quantities more accurately over
long
distances than a Runge-Kutta integration scheme. Results
from
the spatial-Boris integration method and a Runge-Kutta
scheme
are compared for two simulations: (i) a particle in a
uniform
solenoid field and (ii) a particle in a sinusoidally
varying
solenoid field.
In the uniform solenoid case, the spatial-Boris scheme is
shown
to perfectly conserve for any step size quantities such as
the
gyro-radius and the perpendicular momentum. The
Runge-Kutta
integrator produces damping in these conserved quantities.
In the sinusoidally varying case, the conserved quantity
of canonical angular momentum is used to measure the
accuracy
of the two schemes.
For the sinusoidally varying field simulations, error
analysis
is used to determine the integration
distance beyond which the spatial-Boris integration
method is more efficient than a fourth-order Runge-Kutta
scheme.
For beam physics applications where statistical quantities
such as
beam emittance are important, these results imply the
spatial-Boris
scheme is three times more efficient.
P. Stoltz, J. Cary, G. Penn, and J. Wurtele
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