Performance of a High-perveance Electron Gun with a Convex Cathode

A.Shemyakin, G.Kuznetsov, A.Sery, V.Shiltsev, N.Solyak

Fermilab, P.O.Box 500, Batavia, IL 60510, USA

Abstract

Strongly magnetized electron gun with a convex cathode can provide
homogenous transverse current distribution in low temperature electron
beam with high perveance of 5-10 μA/V^3/2^. Such a gun was successfully
tested with currents up to 10 A at the prototype set-up for beam-beam
compensation in the Tevatron collider. In this article we present the
test results. Electron guns of this type can be used in electron cooling
and beam-beam compensation devices.

1.  Introduction

On of the most important characteristics of an electron gun is its
perveance $P = \frac{I}{U_{a}^{\frac{3}{2}}}$$$, where *I* is the beam
current and *U~a~* is the anode potential with respect to the cathode.
For guns with flat or concave cathodes, current density inhomogeneity
becomes large when the perveance exceeds the value of 1 -- 2 μA/V^3/2^.
However, electron beams with higher perveance are needed in number of
applications where charge or current density is a key parameter. One
example is a set-up for compensation of beam-beam effects in high energy
colliders \[1\] where a high-current electron beam needs to be modulated
with high duty factor. Another example is electron cooling at low
energies, where an increase of beam current at a fixed energy increases
cooling rate (see, for instance, \[2\]). For these and similar cases,
where the gun has to be immersed into a strong longitudinal magnetic
field, the perveance can be increased by usage of a convex cathode
\[3\]. Prototype of the gun was tested at the "Tevatron Electron Lens"
(TEL) prototype set-up at Fermilab \[4\]. The paper presents results of
the gun tests.

2   Gun description

The mechanical schematic of the gun is shown in Fig.1 and its main
parameters are listed in Table 1.

The gun is fabricated at Budker INP (Novosibirsk, Russia) and employs a
spherical dispenser cathode made by HeatWave (Watsonville, CA). A
control electrode around the cathode (an analog of the Pierce electrode)
is insolated from the cathode and is used to control the shape of the
current density distribution. The anode shape is optimised for the
maximum smoothness of the radial electric field *E~r~*.

Table 1: Main parameters of the tested gun

  ------------------------------------ ------------------- --------------
  Beam diameter in the gun             10                  mm

  Anode voltage, max                   15                  kV

  Beam current, DC, max                3                   A

  Beam current, pulsed, max            10                  A

  Magnetic field on cathode            0.5- 2              kG

  Control electrode voltage (with      0 - -15             kV
  respect to the cathode)                                  

  Gun perveance                        5.86                μA/V^3/2^
  ------------------------------------ ------------------- --------------

Figure 1: Mechanical schematic of the test bench. Electron gun and beam
analyzer are shown in detail. 1- cathode, 2- control electrode, 3-
anode, 4- water-cooled collector bottom with a 1mm hole in the center,
5- diaphragm with 0.2 mm hole, 6- retarding electrode, 7- analyzer
collector, 8- gun solenoid, 9- drift tube, 10- main solenoid, 11-
collector solenoid.

3 Gun simulation

The gun was simulated and optimised using SSAM code \[5\] in order to
have current density distribution uniform within 10% at gun perveance of
5 μA/V^3/2^. Another important gun parameter is the value of the
electron velocity $\overrightarrow{V_{t}}$ transverse to the magnetic
field. It is convenient to split the velocity into two components:

$\overrightarrow{V_{t}} = \overrightarrow{V_{d}} + \overrightarrow{V_{c}}$
. (1)

Here
$\overrightarrow{V_{d}} = \frac{\overrightarrow{E_{r}} \times \overrightarrow{B}}{B^{2}}c$,
where *B* is the strength of the longitudinal magnetic field in the gun
and *c* is the speed of light, $\overrightarrow{V}d$ denotes the drift
velocity, and $\overrightarrow{V_{c}}$ is the cyclotron component which
is due to cathode temperature and (mostly) transverse electric field on
the cathode \[6\]. In a space free of external electric fields, modules
of both components are constant and $V_{t}$ oscillates with the
cyclotron frequency *eB/mc.* Note, that in this case the value of
$V_{d}$is determined by beam parameters only:

$V_{d} = \frac{2\text{Ic}}{\text{vRB}}$, (2)

where *I* is the beam current, *v* is average z-component of electron
velocity, and *R* is the beam radius. The drift velocity can not be
eliminated in the gun, and it is a natural unit to characterize its
performance. If $V_{c} < V_{d}$, the effective beam transverse velocity
does not depend on the gun optics.

Results of the simulation are shown in Fig.2. The value of the cyclotron
component is less than drift velocity at *B* \> 1 kG.

> ![](media/image1.wmf)Figure2: Results of simulation of the drift and
> cyclotron components at U~a~= 10 kV, I= 5A. The curves represent
> maximum values in the beam in the drift tube.

4 Test bench

Gun characteristics were measured at a test bench (Fig.1) used at
Fermilab for prototyping of the TEL elements. The test bench consists of
the gun immersed into longitudinal magnetic field *B~gun~* of 1- 2 kG
generated by a gun solenoid, a drift tube with diagnostics placed inside
4 kG, 2 m long main solenoid, and a collector, also inside a separate
solenoid. The collector is equipped by a beam analyzer, similar to ones
described elsewhere \[7\]. A small pin-hole (∅ 0.2 mm) in the collector
bottom cuts a narrow flow, which passes through a retarding electrode
and is absorbed by an analyzer collector. By use of steering dipole
corrector coils in the main solenoid one can scan electron beam across
the pin-hole, and the analyzer collector current *I~ac~* recorded as a
function of the beam transverse position reveals the beam current
density distribution.

If the potential of the retarding electrode with respect to the cathode
*U~r~* is close to zero, then only electrons with a high enough
longitudinal momentum $P_{||}$ reach the analyzer collector. Derivation
of the measured function $I_{\text{ac}}(U_{r})$ gives an electron
distribution over a "longitudinal energy"
$E_{||} = \frac{P_{||}^{2}}{2m} - \text{eU}$, where *m* and (*-e*) are
electron mass and charge. \< *should be U~r~* *\>*

5 Results of measurements

Except high perveance, the gun is not much different from a planar
cathode gun. The beam current follows the Child's law with a good
precision. The perveance slightly increases at lower magnetic fields
(5.9 at 2 kG, 6.2 at 0.5 kG).

For the TEL project it is important to control transverse a current
density distribution. The distribution needs to be adjustable preferably
from nearly uniform to a bell-like shape\[1\]. One can do it by
regulation of the control electrode voltage *U~ce~* (Fig.4). At equal
control electrode and cathode potentials ($U_{\text{ce}} = 0$), the
measured gun perveance of 5.9 is slightly higher than 5.6 found in the
simulation . Edge peaks in the current density profile indicate and
computer simulations confirm that the reason is some 0.2 mm protrusion
of the emitted surface from the control electrode in comparison with its
optimum position. The shift occurs because of either uncertainty in the
thermal expansion of the cathode or mechanical misalignment. The effect
can be easily corrected by applying small negative voltage to the
control electrode. With the perveance decreased to its nominal value,
the current density variation in the beam is about 10 %. With further
increase of the absolute value of *U~ce\ ~*, the beam profile approaches
to bell shape.

Distribution of the longitudinal energy of electrons is close to the
Gaussian one:

$\frac{\text{dI}_{\text{ac}}}{\text{dE}_{||}} = \frac{1}{\sqrt{2\pi}} \cdot \frac{I_{\text{ac}0}}{\delta W} \cdot \text{exp}\left\{ - \frac{(E_{||} - E_{0})^{2}}{2{\delta W}^{2}} \right\}$,
(3)

where *I~ac0~* is the maximum value of the analyzer collector current
typically measured at the potential of the retarding electrode equal to
100 V with respect to the cathode. The energy dispersion *δW* and the
shift of the spectrum maximum *E~0~* depend on the beam current (Fig.5)
in a good accordance with known formulae describing relaxation in the
beam \[8\]. In all measurements values of *E~0~* measured in the center
and near beam periphery were equal within precision of measurements,
which was about 1 V at currents up to 1A. The fact implies that the
possible "transverse energy" acquired in the gun is below 1eV.

Described measurements are done in DC regimes. Work with beam currents
above 0.5 A needs a decrease of the collector magnetic field to prevent
thermal problems at the irradiated surface. In such a regime the beam
occupies the collector entrance aperture and can not be shifted for
profile measurements. The maximum current in a DC operation is 3 A and
is limited by cooling of the collector. The system behaviour at higher
currents was investigated in a pulsed regime with the pulse width of
0.2-1 μs. No significant deviation from results of simulations and DC
measurements was found up to the maximum achieved current of 10 A.

6 Conclusion

Results of simulations and measurements show that the gun with a convex
cathode emits a homogeneous beam with perveance of about 6 μA/V^3/2^.
For generation of a 10 A beam, strength of the longitudinal magnetic
field in the gun has to be at least 1 kG. Additional transverse
temperature due to of the specific cathode geometry does not exceed 1 eV
at the beam current of 0.5 A and field strength of 1 kG.

acknowledgements

Original idea of the gun belongs to A.Sharapa who passed away in 1998.
Authors acknowledge participation in gun commissioning of the BINP
(Novosibirsk) team, including A.Alexandrov, P.Logatchov, B.Skarbo,
A.Sleptsov, and B.Sukhina.

REFERENCES

\[1\] V.Shiltsev, et.al, Phys.Rev.ST-AP, 2 (1999), 071001.

\[2\] CERN

\[3\] A.N.Sharapa et al., NIM- A406 (1998), p.169.

\[4\] C.Crawford, et.al, Proc. 1999 PAC, p. 237.

\[5\] D.G. Myakishev, M.A. Tiunov, and V.P. Yakovlev, Int. J. Mod. Phys.
A **2B**(1993) 915

\[6\] D.ryutov, BINP 83-146, Novosibirsk (1983)

\[7\] For example, Kudelainen V.I. et al, , Sov.Phys.JETF, 56 (1982),
p.1191; Alexandrov A.V. et al, , Meas. Sci. Technol. 4 (1993), p.764

\[8\] relaxation