Wilson Prize article: Transverse phase-space manipulations in electron accelerators^*

I am honored and grateful that my contributions to phase-space manipulations in general, and emittance compensation specifically, have been recognized by the Wilson Prize. The purpose of this article is to bring together what I believe to be the most important elements of the broad topic of transverse phase-space manipulations, focusing on the underlying beam physics which enable these types of schemes. We see that emittance compensation can be categorized as an example of the larger class of nonsymplectic manipulations. While the discussion is specifically focused on electron beams, much of the physics can also pertain to ion beams.

Figure 1

For our purposes, a beam is a collection of particles that mostly go in the longitudinal, or $z$, direction, but with some transverse motion in the $x$ and $y$ directions.

Figure 2

Comparison of a phase-space distribution of particles (dots) and the equivalent hard-edged rms beam (uniform density within the red ellipse). This figure is courtesy of William Barletta.

Figure 3

Kehne’s PhD thesis experiment. (Top) experimental setup; (middle) description of the five beamlets; (bottom) relative emittance growth due to nonlinear free energy. (Images from [9].)

Figure 4

Numerically modeled radial phase space of a beam in an induction linac [10]. (Top left) just after the electron gun, about 4 MeV; (top right) after a few MeV of acceleration and betatron periods; (bottom) at the end of the linac, about 20 MeV; images are from [10].

Figure 5

Illustration of how the horizontal phase space can be twisted along the bunch’s axial direction.

Figure 6

(Left) bunch initially with uniform radius; (right) the center slice (purple) will expand more than the end slices (red) due to a higher space-charge force.

Figure 7

One of Peterson’s figures from [15] showing the initial (just after the tapered foil) and final horizontal phase spaces (top) and the initial and final $x$-energy correlations (bottom).

Figure 8

Starting at the same radius (where the red and purple circles touch), the edge of the end slice will oscillate about a smaller radius (red circle) than the edge of the middle slice (purple circle). The electron orbits are clockwise in radial phase space, and the boundary of the bunch’s projected phase space is represented by the black triangle after the bunch drifts a while. As the colored circles represent the radii of the edges of the center and edge slices, other particles from those slices lie on the two mostly horizontal black lines.

Figure 9

SLAC simulations (from [19]) verifying the ability to compensate the emittance growth from axially dependent space-charge forces. The numbers in the plot indicate the location of the lens in cm.

Figure 10

Experimental BNL measurements (from [20]) showing the slice phase-space ellipses of the front, middle, and end slices, for solenoid currents of 102 A (a), 106 A (b), and 110 A (c). As predicted, the slices rotate relative to each other as the solenoid focal length is changed. The projected emittance is minimized at a solenoid current of 106 A.

Figure 11

Optimized rf photoinjector design using the Ferrario working point, from [11].

Figure 12

Flat-beam transform configuration. A solenoid generates an axial magnetic field at the location of the cathode. Once the beam leaves the solenoidal field, it encounters three skew quadrupole which remove the $x-y$ correlations. This figure is courtesy of Kip Bishofberger.

Figure 13

Emittance evolution in the LCLS injector operated as an FBT where eigp is the higher (“plus”) eigen-emittance, eigm is the lower (“minus”) eigen-emittance, and the $x$ and $y$ projected emittances lie on top of each other (from [36]).

Figure 14

More modern concept of the Bovet/Peterson emittance reduction technique. Reference [36] used this configuration to develop a scheme to transfer excess transverse emittance into the longitudinal direction both to reduce the transverse emittances and to provide a substitute for the laser heater for the LCLS accelerator. The image is from [42].