Field Stability Issue for No
r
mal Conducting Cavity
under Beam Loading
Rihua Zeng,
2013
‐
04
‐
26
Introduction
There is cavity field ‘blip’ at the beginning of beam loading (~several ten micro

seconds)
under PI control feedback for normal conducting
cavities. It occurs even
if cavity field
amplitude
and phase
are
set careful
ly
to the same nominal value
s
before beam coming.
The solution to this problem is to adjust the beam i
njection time, having the beam
injected before the cavity field get
s
constant and cancell
ing each other the voltages
induced by beam and induced by generator current. In the case of beam injection time
unable to adjust, feedforward compensation for corresponding beam mode help
s
solve the
problem.
Simulation background and parameters
Under the
matching
condition of
a beam

loaded
cavity
operation
, the reflection power in
the steady state is zero, and the coupling
factor can be calculated from
the generator
power and the
power transferred to the beam
[1]
:
!
!"#
=
!
!
!
!
=
!
!
!
!
!
!
!
.
There
fore, some parameters used in the simulation of normal conducting cavity is
calculated as follows given some known values (
for DTL tank 2, energy gain
:
19.5MeV
,
required power:
2.12 MW
, Q
0
: 56000
)
:
The coupling factor
!
!"#
and the shunt impedance R under matching condition can be
calculated
as well
from the following equations
[2]
:
!
!"#
=
1
+
2
!"
!
!
!"#
!
!
!
!"#
!
!
=
!
!"#
∙
!
!"#
!
2
!
where,
!
!
is the synchronous phase,
!
!"#
is the cavity voltage, and
!
!
!
is the average
DC
beam current.
In the simulation in this note, the cavity field in the case without beam is always kept
constant by feeding a proper feedforward signal and frequency tracking in the filling
stage to keep filling on resonance.
Cavity field ‘blip’ at beam loading
If the cavity field is kept constant at first and then beam comes causing perturbation to
cavity field, the c
avity field ‘blip’ at the beginning of beam loading (~several ten micro

seconds) is inevitable under PI contr
ol feedback
for normal conducting cavities
due to the
following
factors
[3]
:
There is an unavoidable loop delay, in the order of 2
µ
s.
Relatively much low Ql
for normal conducting cavity, around a factor of 30
lower than superconducting cavity. Beam loading perturbations is much larger
than superconducting cavity in t
he first couple of micro

second
s
(loop delay and
feedback loop bandwidth
limit
).
In PI contro
ller for normal conducting cavity, the gain of proportional controller
is very low (<5) and the performance of integral controller
degrades in the high
frequency perturbations
.
Figure 1
and Figure 3 show
the remained ‘blip’ under PI feedback. The ‘blip’
is quite
large, ~10% error in amplitude, and 2.5
°
in phase.
Figure 2 shows f
urther information of
occurrence
of beam loading perturbations
, which reveals that the perturbation occurs
despite that the phase and amplitude
are
set to the target value
s
before
beam coming
.
When the
perturbation
is too
large
,
adding
another adaptive feedforward loop
(by nature a
pulse

to

pulse feedback loop) might not totally eliminate the
beam loading
perturbation,
body
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