Field Stability Issue for Normal Conducting Cavity under Beam ...

sublimefrontUrban and Civil

Nov 15, 2013 (3 years and 4 months ago)

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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