Design study of a low-emittance high-repetition rate thermionic rf gun

We propose a novel gridless continuous-wave radiofrequency (rf) thermionic gun capable of generating nC ns electron bunches with a rms normalized slice emittance close to the thermal level of 0.3 mm mrad. In order to gate the electron emission, an externally heated thermionic cathode is installed into a stripline-loop conductor. Two high-voltage pulses propagating towards each other in the stripline-loop overlap in the cathode region and create a quasielectrostatic field gating the electron emission. The repetition rate of pulses is variable and can reach up to one MHz with modern solid-state pulsers. The stripline attached to a rf gun cavity wall has with the wall a common aperture that allows the electrons to be injected into the rf cavity for further acceleration. Thanks to this innovative gridless design, simulations suggest that the bunch emittance is approximately at the thermal level after the bunch injection into the cavity provided that the geometry of the cathode and aperture are properly designed. Specifically, a concave cathode is adopted to imprint an Ƨ-shaped distribution onto the beam transverse phase-space to compensate for an S-shaped beam distribution created by the spherical aberration of the aperture-cavity region. In order to compensate for the energy spread caused by rf fields of the rf gun cavity, a 3rd harmonic cavity is used. A detailed study of the electrodynamics of the stripline and rf gun cavity as well as the beam optics and bunch dynamics are presented.

Figure 1

A schematic of the proposed HV pulse-gated thermionic rf gun. The inset shows the cathode assembly and the on-axis region of an accelerating gun cavity. A cylindrical single-crystal ${\mathrm{CeB}}_6$ cathode of radius $r_c$, schematically shown by the red rectangle, is installed into the central conductor of a stripline-loop. The wall of the gun cavity embodies the outer conductor of the stripline-loop so that electron bunches are injected to the gun cavity through an aperture in this part of the outer conductor. The input aperture radius is $r_g$ and the radius of the output cavity aperture is $a$. The accelerating gaps of the stripline-loop and cavity are $h$ and $d$, respectively. The cathode can be heated by a DC laser or a diode DC electron gun labeled as the heater in the inset. The dotted red lines represent schematically the rays from the laser heater or the trajectories of electrons emitted by the electron heater.

Figure 2

On top, a 2D cross-sectional—in the electron bunch plane—drawing of the symmetrical stripline-loop based cathode configuration. The inner conductor and vacuum region are depicted in white and blue, respectively. The cathode is schematically shown by the red rectangle located in the inner conductor. On bottom, a cross-sectional drawing of the stripline-loop in perspective.

Figure 3

Two cross-sections of the stripline-loop: (a) plane $xz$ across the cathode, (b) plane $xy$ across the feeding stripline. The gray rectangular areas represent the inner conductor of the stripline-loop (upper plot) and the feeding stripline (bottom plot). The cathode is shown by the red rectangle. In the feeding stripline the position of the inner conductor is symmetrical whereas in the stripline-loop the inner conductor is displaced in order to provide a higher voltage in the cathode–gate-electrode gap.

Figure 4

The forward and transmitted pulses at the feeding port.

Figure 5

The electric (top) and magnetic (bottom) field distributions in the stripline-loop at the moment when the middle of the pulse passes the cathode. The magnetic fields cancel each other. The simulation is performed with the CST microwave studio.

Figure 6

The electric field profiles on the cathode surface along (red) and across (blue) the inner conductor. The dotted black curve represents the analytical approximation (1).

Figure 7

A family of curves (black) of the longitudinal electric field $E_z(x,z)$ for different $z$ as a function of $x$. The field is shown in the cross section orthogonal to the conductors of the stripline-loop and drawn through the cathode, see the upper drawing in Fig. 3. For $z<1$ the field extends over the region from $-10\mathrm{mm}$ to 10 mm, which corresponds to the interior space of the stripline-loop, whereas for $z\ge 1$ the field is limited to the space inside the aperture channel. The blue curves depict the envelope of the electron beam.

Figure 8

The geometry and electric field distribution in the rf gun cavity designed with SUPERFISH.

Figure 9

The longitudinal electric field profile along the accelerating gap of the gun cavity. The accelerating potential is 36.533 kV.

Figure 10

The gun geometry used in egunsimulations. The electrostatic equipotential lines are coded by color such that dark blue and dark red correspond to the maximum negative and zero potential, respectively.

Figure 11

The profile of the longitudinal electric field in the gun vs. distance. The simulation is perform with egunfor the whole interaction region from the cathode, $z=0\mathrm{mm}$, to the end of output aperture of the cavity, $z=38\mathrm{mm}$. The electric field on the cathode produced by the HV pulser is $10\mathrm{MV}/\mathrm{m}$. The aperture region extends from $z=1\mathrm{mm}$ to $z=7\mathrm{mm}$, where the absolute value of the field has an extremum.

Figure 12

The normalized rms emittance in mm mmrad (blue curve with dots), the beam envelop in mm (dotted black) and radial electric field distribution at $r=1\mathrm{mm}$ in $\mathrm{MV}/\mathrm{m}$ (solid red) vs. the longitudinal position. The results are obtained with egun.

Figure 13

Gain in the deflecting voltage in the accelerating stripline gap (dotted blue curve), the aperture channel (dashed black curve) and the sum of the two (solid red curve) vs transverse coordinate.

Figure 14

Phase-space of a beam of straight rays (dotted black) and a realistic beam (solid blue) at $z=3.5\mathrm{mm}$.

Figure 15

A set of distributions of the longitudinal (upper plot) and transverse (bottom plot) electric field as function of the radial distance for different longitudinal positions. The solid curves depict solutions to the Poisson equation whereas the dotted curves are solutions to the Laplace equation. The beam envelope with the arrow pointing out the direction of increasing $z$ is also depicted.

Figure 16

Gun geometry with the optimized cathode profile.

Figure 17

The normalized rms emittance in mm mmrad for a flat and concave cathode vs. the longitudinal distance. The thermal emittance is shown as a reference.

Figure 18

Beam optics in the vicinity of a concave cathode.

Figure 19

Transverse phase-space of a beam next to the concave cathode. The curve and dots stand for the analytical and numerical results, respectively.

Figure 20

Beam phase-space in the plane of the electric wall of the input aperture. The cathode is flat; the emittance is 0.423 mm mrad.

Figure 21

Beam phase-space in the exit plane of the input aperture. The cathode is flat; the emittance is 1.9 mm mrad.

Figure 22

Beam phase-space in the plane of the electric wall of the input aperture. The cathode is concave; the emittance is 1 mm mrad.

Figure 23

Beam phase-space in the exit plane of the input aperture. The cathode is concave; the emittance is 0.243 mm mrad.

Figure 24

Emittance vs. current for a flat and concave cathode.

Figure 25

The bunch phase-space at the output of the rf gun cavity. The cathode is concave.

Figure 26

A comparison of the transverse phase-spaces of the bunch for the flat (bottom left) and concave (bottom right) cathodes at the end of the rf gun cavity. The bunch distribution (top) is represented by 9 consecutive slices along the bunch marked by different colors.

Figure 27

The bunch phase-space at the output of the 3rd harmonic cavity. Top left: transverse phase-space of slices, top-right: transverse position of electrons vs rf phase, bottom left: transverse distribution of particles; bottom right: longitudinal phase-space.

Figure 28

Snapshots of the electron distributions in the $rz$ plane.

Figure 29

Transverse phase-space of 9 consecutive slices without taking into account the initial thermal emittance.