Noninvasive beam-size measurements for linear induction accelerators

Diamagnetic loops (DML) can be used as a noninvasive method for the measurement of beam size in electron beam accelerators that use solenoidal magnetic transport. The loop fundamentally measures the magnetic flux excluded by a diamagnetic object. A comprehensive theory relates the rms beam radius to the excluded flux measured by the DML. We have built and calibrated a DML apparatus. Recently, this DML has been used to measure the size of the electron beam near the final focus of a flash-radiography linear induction accelerator. The results are in agreement with predictions from transport code simulations. In this article, we review and summarize the construction, calibration, and electron-beam testing of this DML.

Figure 1

Magnetic fields inside diamagnetic loop diagnostic. $B_0$ is the field prior to the arrival of the beam. The field is depressed inside the beam by its diamagnetism. Outside of the beam, the field is increased by $\mathrm{\Delta }B$ to conserve flux (Adapted from Ref. [14]).

Figure 2

DML apparatus. The bias solenoid is shown in purple. The beam pipe is shown in blue and the flux-conserving outer wall is shown in gray. Balanced-loop signal output cables are shown in green (Adapted from Ref. [21]).

Figure 3

Magnetic bias field on axis of the DML apparatus for differing values of the solenoid drive current, as indicated in the legend.

Figure 4

Magnetic field of calibration coil in the DML apparatus as calibrated.

Figure 5

DML installation in DARHT-I downstream transport.

Figure 6

Integrated loop-flux signal from a shot with 200-G bias field (green curve) compared with the integrated loop-flux signal from a background shot with zero bias field (red curve). (The baseline errors long after the pulse are due to the first-order approximation to correction for cable distortion).

Figure 7

Excluded flux (green curve) and flattop beam current (black curve). The data for this plot were from shot 37858 corrected for a background shot 37853.

Figure 8

Beam rms radius measured by the DML for shot 37858.

Figure 9

Comparison between the rms radius calculated by hand using DAAAC (black curve) and our idl [25] code dml22zeta.pro (red curve) for shot 37858. (Note the expanded time scale).

Figure 10

Average excluded flux as a function of DML bias field for the three peak fields of the DT-1 focusing solenoid. Dotted lines are least-square fits of linear dependence on the bias field.

Figure 11

Beam envelope radius predicted by the xtr code for the maximum DT-1 magnetic field (1.45 kG) and the minimum DT-1 field (0.80 kG) used for these experiments (red curves). Also shown are DST solenoid fields on axis (green curves) and the beam pipe wall (cyan lines). (DT-1 field for maximum beam size is shown). BPM locations are marked with blue dashed lines.

Figure 12

Tuning curve for DT-1 focusing solenoid showing the beam rms radius predicted by xtr at the DML location for a normalized 4-rms emittance of 0.071 cm rad (blue curve). DML measurements of rms radius averaged over flattop are plotted in red.

Figure 13

Beam rms radius for the three settings of the DT-1 focusing solenoid; peak $B=0.80\mathrm{kG}$ (red curve), peak $B=1.13\mathrm{kG}$ (blue curve), and peak $B=1.45\mathrm{kG}$ (black curve).

Figure 14

Average of beam rms radii calculated for ten shots with DT-1 set for a peak field of 0.80 kG (blue curve). These included shots with the DML bias field set to 50, 100, and 200 G. Also shown in cyan is the average $\pm 1$ standard deviation as an indication of the uncertainty of the measurement.

Figure 15

Flux resulting from offset-tilt effect (green curve) compared with background flux (red curve). The offset-tilt flux is only shown during the current flattop because the calculation is subject to large timing error during the beam rise and fall. (This zero-bias shot 37853 was used as background for shot 37858 analysis).