BBU threshold current study for 6 GeV beam in 12 GeV beamline setup
Ilkyoung Shin and Byung C. Yunn
JLAB-TN-09-004
January 12, 2009
1. Introduction
The study of BBU threshold current is done for a 6 GeV beam in a 12 GeV beamline because the
beam of 6 GeV will be still needed after 12 GeV upgrade. In this work, instead of 6 GeV, 6.6
GeV are considered to compare three beamline setups which are 3-pass 6.6 GeV, 5-pass 6.6
GeV, and 5-pass 11 GeV.
2. Assumption and simplification in simulations
The same assumptions, simplification, and treatment as in TN-04-035 and TN-07-069 are used in
the simulations. Two interesting quantities are Ql=107 and R/Q = 82.5 Ohms. Only 1874 MHz
mode is excited in cavities.

The 7-cell cavity cryomodules are located at the 21st ~ 25th zones in the North linac and
the 46th ~50th zones in the South linac.

The 1874 MHz mode is excited in the 7-cell cavities.

Threshold currents are calculated when Ql = 107 and R/Q = 83 Ohms.

Only the 7-cell cavities are exited with the 1874 MHz mode in each threshold calculation
while the other cavities give energy gains without excitation of the HOMs.

DBA arc optics are used.

The total recirculation path length is 6554(6549, 6547, 6546) RF wavelengths for the 1st
(2nd, 3rd, 4th) pass of the CEBAF accelerator.
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3. Two beamline setup for 6 GeV
The 12 GeV nominal beamline setup is 5-pass 11 GeV, and each linac has a 1.1 GeV energy
gain. On the other hand, the 5-pass 4 GeV setup has a 0.4 GeV energy gain in each linac.
3.1. 3-pass 6 GeV setup
3 passes of the electron beam goes through 6 linacs. If the nominal energy gain of 12 GeV
setup, which is 1.1 GeV, is taken into account, the total energy gain is 6.6 GeV.
(Energy gain during 3-pass) = (energy gain in a linac) χ (number of linacs during 3-pass)
6.6 GeV
=
1.1 GeV
χ
6 linacs
In this study, 3-pass 6 GeV will beam 3-pass 6.6 GeV.
3.2. 5-pass 6 GeV setup
The 60% version of 12 GeV setup is the 5-pass 6.6 GeV setup. The energy gain in linacs and
injection energy are reduced to 60% of the 12 GeV setup values.
Energy gain during 5 pass = energy gain of 12 GeV nominal setup χ
6.6 GeV
=
χ
11 GeV
60
100
60
100
As above, 5-pass 6 GeV means 5-pass 6.6 GeV.
3.3. Injection energy
Injection energy satisfies the equation
(Injection energy)
=
9
80
χ (energy gain of a linac).
By substituting the actual values into the formula, injection energies are obtained.
Injection energy for 4 GeV setup =
Injection energy for 12 GeV setup =
2
9
80
9
80
χ
400 MeV =
χ 1.1 GeV
45 MeV
= 123 MeV
4. Simulation results
4.1. 3-pass 6.6 GeV
Threshold current = 0.537 mA, Injection energy = 123 MeV
Figure 1. 3-pass 6.6 GeV
4.2. 5-pass 6.6 GeV
Threshold current 0.131 MeV, Injection energy = 73 MeV
Figure 2. 5-pass 6.6 GeV
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4.3. 5-pass 12 GeV
This work is done in TN-08-069.
Threshold current 0.219 mA, Injection energy 123 MeV
Figure 3. 5-pass 12 GeV
5. Comparison of threshold currents with 3-pass and 5-pass setups
The simulation results are summarized in the table.
3-pass 6.6 GeV
5-pass 6.6 GeV
5-pass 11 GeV
Threshold current
0.537 mA
0.131 mA
0.219 mA
Injection energy
123 MeV
73 MeV
123 MeV
Table 1. Simulation results
The threshold current for the 3-pass 6.6 GeV is greater than for the 5-pass 6.6 GeV. Let us
compare the 5-pass 6.6 GeV with the 5-pass 12 GeV. As the beam energy is reduced from 11
GeV to 6.6 GeV, which is 60% reduction, the threshold current and injection energy are also
decreased to approximately 60%. The threshold current is proportional to the injection energy
while the number of pass is fixed.
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6. Availability of the maximum current
The maximum beam current is limited by the beam dump power.
(Beam dump power) ≥ (maximum beam current) χ (maximum beam energy ∕ e)
Applying the maximum beam dump power, 1 MW, to the formula gives
1 MW ≥ 0.151 mA χ 6.6 GeV ∕ e
We have maximum beam current of 0.151 mA. The table below shows the maximum beam
current and the threshold currents of the 6.6 GeV setup.
Maximum beam current
by beam dump power
Threshold current for
3-pass 6.6 GeV
Threshold current for
5-pass 6.6 GeV
0.151 mA
0.537 mA
0.131 mA
Table 2. Comparison of threshold currents with maximum available beam current
The maximum beam current is not available in the 5-pass 6.6 GeV setup because the threshold
current, 0.131 mA, is less than the maximum beam current, 0.151 mA. Maximum beam current
is available for the 3-pass 6.6 GeV setup.
7. Conclusions

The threshold current for three setups are:
Threshold current
3-pass 6.6 GeV
5-pass 6.6 GeV
5-pass 11 GeV
0.537 mA
0.131 mA
0.219 mA
Table 3 Threshold current for three setups


The threshold current is proportional to the injection energy at the same number of
passes. Therefore, the threshold current for the 5-pass 6 GeV setup will be a factor of
0.55 for 5-pass 11 GeV setup.
The maximum beam current is not available in the 5-pass 6.6 GeV setup.
8. Acknowledgement
Thanks a lot to Ryan Bodenstein.
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