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Preliminary results for electron
lens with beam current of 20 A
A. Barnyakov, D. Nikiforov, A. Levichev
BINP-CERN, 18.10.2016
[email protected]
Equilibrium beam radius
Equilibrium radius is the constant radius for the beam, which it will has in the uniform
magnetic field. It depends on the cathode radius Rc, magnetic field on the cathode Bc,
beam current I, beam voltages U and magnetic field in the channel B (Appendix 1)
Cathode field 0.2 T
To obtain the beam
diameter of 2 mm
in the magnetic
field of 5 T the
cathode radius has
to be 5 mm with
cathode magnetic
field of about 0.2 T
and beam potential
of 10-35 kV
Estimation of the maximum of the vacuum
tube perveance for thin beam Rb<<Rt
The main problem for propagation through the vacuum chamber of
high current beam with low energy is virtual cathode inside the vacuum
chamber. This effect can be estimated with help of maximum tube
perveance. For thin beam the beam and tube can be presented as
cylindrical capacitor and the tube perveance can be estimated as (see
Appendix 2)
2
4 0
Pt 
3 3 ln Rt Rb
  e / m  17.58  1010[C / kg]
Vacuum tube and beam perveance
I=20, U=10 kV microperveance is 20, Rt/Rb=1
I=20, U=25 kV microperveance is 5, Rt/Rb<12.5
I=20, U=35 kV microperveance is 3, Rt/Rb<40
With tube aperture of 80 mm to obtain the beam diameter of
about 2 mm the beam voltage must be about 35 kV
Magnetic field in the solenoids
Equilibrium diameter of the beam with I=20 and V=10-35 kV
for magnetic field of 5 T is about 2 mm for the cathode radius
of 5 mm and cathode magnetic field of 0.2 T
Beam dynamics I=20 A, V=25 kV
In high magnetic field of the bending solenoid the beam is compressed and when
the ratio Rt/Rb>12.5 the virtual cathode is arisen. To remove this effect without
changing the aperture of vacuum chamber and beam current the beam potential
has be increased (~35 kV). For the cone type chamber the ratio Rt/Rb>12.5
becomes earlier and such design is worse than tube with constant radius.
Possible design of electron gun with 35 kV and 20 A
Beam current is I=20 A
Voltage is 35 kV
Magnetic field is 0.2 T
Cathode radius is 5 mm
Electron gun with 35 kV and 20 A
Gun parameters
Cathode diam.
10 mm
Cathode material
Ir-Ce
Energy
Up to 35 kV
Current
21 A
Tr. Profile
Flat top
Emit (gun exit)
7.8 mm mrad
Beam dynamics I=20 A, V=35 kV
All current (20 A)
propagates through
the electron lens
Beam dynamics I=20 A, V=35 kV
Beam potential is decreased when the beam is compressed and
inputted in the vacuum chamber with high aperture of the
bending solenoid. Due to asymmetric vacuum chamber the beam
potential becomes also asymmetric and particles get different
velocities.
Beam dynamics I=20 A, V=35 kV: transverse beam space
Due to asymmetric vacuum chamber the beam profile is also asymmetric. For particles
with different potential the Lorenz radius are differed. Besides the individual rotation
for every particle the beam is rotated as a whole due to magnetic field on the cathode
therefore the potential distribution along the radius is changed during the time.
Beam dynamics I=20 A, V=35 kV: energy of the particles
30 kV
10 kV
Beam dynamics I=20 A, V=35 kV: conclusion
1. The initial beam potential of 25 kV is not enough for beam current of 20 A and
vacuum tube aperture of 80 mm.
2. For vacuum tube aperture of 80 mm and beam current of 20 A the initial beam
potential has to be about 35 kV.
3. To compress beam down to 2 mm by magnetic field of 5 T the cathode
diameter has to be about 10 mm with magnetic field of 0.2 T. Reducing the
cathode magnetic field allows the cathode diameter to be increased.
4. Increasing of the ratio between transverse size of the vacuum chamber and
beam size decreases the beam potential.
5. Asymmetric vacuum chamber leads to asymmetric distribution of the potential
of the particles and profile of the beam.
6. For single particles the potential can be reduced down to 9 kV in the vacuum
tube with aperture of 80 mm and beam diameter of about 3 mm. In this case
the average beam potential is about 20 kV.
7. Due to nonuniform beam potential the velocities of the particles are differed,
the front of the beam can be increased and particles motion is not laminar.
8. The typical beam size in the main solenoid is about 3 mm. Most likely, to
decrease this size the new design of the bend can be needed.
9. Needs to investigate of 10 mm cathode lifetime (See Appendix 3).
Beam dynamics I=20 A, V=35 kV: vacuum chamber
symmetrization
Symmetrization of the vacuum chamber can
improve the beam potential
Beam dynamics I=20 A, V=35 kV: vacuum chamber
symmetrization
30 kV
More particles
have potential less
than 20 kV
10 kV
30 kV
Potential
distribution is
more uniform
12 kV
Beam dynamics I=20 A, V=35 kV: vacuum chamber
symmetrization
Transverse beam space
Beam dynamics I=20 A, V=35 kV: vacuum chamber
symmetrization
Conclusion:
1. Symmetrical vacuum chamber can improve the beam
potential distribution
2. More uniform beam potential can reduce transverse
beam size
3. For this solution the design of the vacuum chamber has
to be changed and, may be, bend design too
4. Needs more investigation to choice and optimize new
design
Additional researches: beam propagation not
along solenoid axis
Taking into account high magnetic field the beam will go along the magnetic field force
lines. In the center of the solenoid, the beam will move rectilinearly due to high radiuses
of the solenoid. In the end of the magnet the beam will have some angle which is excited
by magnetic field force lines. Additional corrector can compensate this angle.
Additional researches: compensation of the
electron beam field by proton field
Proton beam
with electron
beam
Electric field from the electron beam is
up to 1.6 MV/m
There is no
influence of the
proton field on the
electron field due to
ultra relativistic
energy of proton
(relativistic factor is
about 7000)
Electric field from the proton beam is
up to 22 kV/m
Additional researches: collimator with wires
Current is 230 A with the same direction,
maximum magnetic field is 0.01 T
Thank you for the attention
Appendix 1: equilibrium beam radius in
magnetic field


2
2I
1 1
Rc
 Bc  
Req 


1

4
  
3/ 2
2
2
2
0
UB
B 
2I
   3 / 2 U B 2
0

  e / m  17.58  10 [C / kg]
10
I – beam current
U – beam potential
Bc – magnetic field on the cathode
Rc – radius of the cathode
B – magnetic field in the transport
channel







4
Appendix 2: maximum of the tube perveance
Appendix 3: IrCe Current density vs.
Temperature