Note on numerical study of the beam energy spread in NDCX-I
The kinetic energy spread (defined here as the standard deviation of the beam particle energies) sets the ultimate theoretical limit on the longitudinal compression that can be attained on NDCX-I and NDCX-II. Experimental measurements will inevitably include the real influences on the longitudinal phase space of the beam due to injector and accelerator field imperfections1. These induced energy variations may be the real limit to the longitudinal compression in an accelerator. We report on a numerical investigation of the energy spread evolution in NDCX-I; these studies do not include all the real imperfections, but rather are intended to confirm that there are no other intrinsic mechanisms (translaminar effects, transverse-longitudinal anisotropy instability, etc.) for significant broadening of the energy distribution. We have performed Warp simulations that use a realistic Marx voltage waveform which was derived from experimental measurements (averaged over several shots), a fully-featured model of the accelerating and focusing lattice, and new diagnostics for computing the local energy spread (and temperature) that properly account for linear correlations that arise from the discrete binning along each physical dimension (these capabilities reproduce and extend those of the earlier HIF code BPIC). The new diagnostics allow for the calculation of multi-dimensional maps of energy spread and temperature in 2-D axisymmetric or 3-D Cartesian space at selected times. The simulated beam-line was terminated at z = 3 m by a conducting plate, so as to approximately reproduce the experimental conditions at the entrance of the spectrometer that was used for mapping the longitudinal phase space. Snapshots of the beam projection and current, as well as the Marx waveform and history of beam kinetic energy collected at the end plate, are shown in Fig. 1. A two-dimensional axisymmetric map of energy spread from simulations of a typical NDCX-I configuration is shown in Fig. 2 (a). The energy spread starts at 0.1 eV at the source and rapidly rises to a few eV, then fluctuates between a fraction of an eV and tens of eV, ending near the exit in a range of a few eV at the outer edge of the beam to a few tens of eV near the axis. The higher value on-axis is associated with greater numerical noise there, due to the axisymmetric geometry of the calculation, resulting in poorer simulation-particle statistics at small radius. A scatter plot of the macroparticles kinetic energy (KE) versus radius (R) and longitudinal position (0.28 m < z < 3 m) colored by local energy spread is shown in Fig. 2 (b). As expected, there is a correlation of the kinetic energy with radius that is clearly visible at z = 2.8 m and vanishes at the metal plate at z = 3 m. More snapshots from simulations varying the time step, grid resolution and number of macroparticles are given in Appendix II. The macro-particles were collected at the exit plate and their kinetic energy history is plotted in Fig. 3 (left) and contrasted to an experimental measurement using a streak camera shown in Fig. 3. For some types of measurements, averaging over several pulses to improve signal-to-noise will contribute an additional spread that may not be present on any single beam pulse. The upper bound for the energy spread is in the range of a few 100 eV for the experiment while in the range of a few eV for the reported Warp simulations. The Marx voltage exhibits variations in the range of up to several hundreds of volts, playing a significant role in the experimentally measured energy spread, which may account for the difference between the experimental and the simulated bounds.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- Accelerator& Fusion Research Division
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 1007225
- Report Number(s):
- LBNL-4288E; TRN: US1101500
- Country of Publication:
- United States
- Language:
- English
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