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Title: Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model

Abstract

The Pulse-Line Ion Accelerator (PLIA) is a promising approach to high-gradient acceleration of an ion beam at high line charge density [1, 2, 3, 4, 5, 6]. A recent note by R. J. Briggs [7] suggests that a ''sheath helix'' model of such a system can be solved numerically in the quasi-static limit. Such a model captures the correct macroscopic behavior from ''first principles'' without the need to time-advance the full Maxwell equations on a grid. This note describes numerical methods that may be used to effect such a solution, and their connection to the circuit model that was described in an earlier note by the author [8]. Fine detail of the fields in the vicinity of the helix wires is not obtained by this approach, but for purposes of beam dynamics simulation such detail is not generally needed.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
893987
Report Number(s):
UCRL-TR-218776
TRN: US0700014
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; ACCELERATION; ACCELERATORS; BEAM DYNAMICS; CHARGE DENSITY; ION BEAMS; MAXWELL EQUATIONS; SIMULATION

Citation Formats

Friedman, A. Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model. United States: N. p., 2006. Web. doi:10.2172/893987.
Friedman, A. Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model. United States. doi:10.2172/893987.
Friedman, A. Wed . "Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model". United States. doi:10.2172/893987. https://www.osti.gov/servlets/purl/893987.
@article{osti_893987,
title = {Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model},
author = {Friedman, A},
abstractNote = {The Pulse-Line Ion Accelerator (PLIA) is a promising approach to high-gradient acceleration of an ion beam at high line charge density [1, 2, 3, 4, 5, 6]. A recent note by R. J. Briggs [7] suggests that a ''sheath helix'' model of such a system can be solved numerically in the quasi-static limit. Such a model captures the correct macroscopic behavior from ''first principles'' without the need to time-advance the full Maxwell equations on a grid. This note describes numerical methods that may be used to effect such a solution, and their connection to the circuit model that was described in an earlier note by the author [8]. Fine detail of the fields in the vicinity of the helix wires is not obtained by this approach, but for purposes of beam dynamics simulation such detail is not generally needed.},
doi = {10.2172/893987},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2006},
month = {Wed Feb 01 00:00:00 EST 2006}
}

Technical Report:

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  • This note describes a simple model developed to explore some of the properties of the pulse-line ion accelerator [1], here represented as a series of lumped elements, in the general parameter regime for the ''NDCX-1d'' experiments. The goals of this modeling are: to understand the evolution of various possible input pulses in the presence of dispersive effects and imperfect termination of the line; to examine scenarios for beam acceleration; and to explore the effects of ''beam loading'', that is, changes to the voltages along the helical line that result from the interaction of the beam's return current with the ''circuitry''more » of that line. In Section 1 below, the model is described and the method of solution outlined; in Section 2, a low-current example of beam acceleration is presented; in Section 3, runs are presented showing the development of beam loading-induced voltages as model pulses are followed; in section 4, the modeling of a higher-current beam under acceleration is presented, and the effects of beam loading quantified; and in section 5, a brief summary of complementary efforts and of plans to extend the modeling is presented.« less
  • The Pulse-Line Ion Accelerator (PLIA) is a helical distributed transmission line. A rising pulse applied to the upstream end appears as a moving spatial voltage ramp, on which an ion pulse can be accelerated. This is a promising approach to acceleration and longitudinal compression of an ion beam at high line charge density. In most of the studies carried out to date, using both a simple code for longitudinal beam dynamics and the Warp PIC code, a circuit model for the wave behavior was employed; in Warp, the helix I and V are source terms in elliptic equations for Emore » and B. However, it appears possible to obtain improved fidelity using a ''sheath helix'' model in the quasi-static limit. Here we describe an algorithmic approach that may be used to effect such a solution.« less
  • A numerical solution was developed to find the aboveground late-time magnetic fields resulting from a surface nuclear burst. The time derivative in Maxwell's magnetic curl equation was ignored and the result was expressed in integral form using Stokes' law. This expression is expanded in spherical coordinates, the radical Compton current and the radical conduction current source terms were calculated, using the time-independent code, and the polar integrals were calculated. Magnetic field values were calculated and compared with analytic expression. For r < 2 Km, the results differed by less than 2.7. However, for r > 2 Km, the numerical valuesmore » were an order of magnitude larger. The electric and magnetic field calculations were then used to test the spatial and temporal regions of validity of the simplified boundary condition and the quasi-static approximations. The assumption that the ground conductivity greatly exceeds the air conductivity leads to a simplified boundary condition at the earth's surface (E sub r = 0), and, in turn, to an inner radial limit to the validity of the results. The quasi-static approximation that the electric fields be derivable from a scalar potential determines the time regime over which the results are valid. The computer program included in this report is useful for late-time EMP calculations because of the short execution time and its wide range of applicability.« less