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

Urban and Civil

Nov 15, 2013 (4 years and 7 months ago)

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Field  Stability  Issue  for  No
r
mal  Conducting  Cavity

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
-
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.

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
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

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

, 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
,

(by nature a
pulse
-
to
-
pulse feedback loop) might not totally eliminate the
perturbation,
which
might be one of reason
at SNS where the ‘blip’ is still th
ere after applying the
‘learning’ feedforward.

Figure
1

Cavity field stability issue under PI feedback control

0
1
2
3
4
5
x 10
ï
3
0
5
10
15
20
25
Amplitude / MV
Time / s
Cavity Field

Figure
2

IQ signals of s
et points and

real

cavity field

output

under PI feedback control in simulation (yellow &
pink: I&Q signal of set points, green & red: I&Q signals of cavity field)

Possible  solution

One possible solution is to adjust the beam injection time, cancelling each other the
voltages induced by beam
and induced by generato
r current, like the proposed solution
in
superconducting cavities

in other accelerators
. The cavity field will maintain constant as
soon as the beam is injected at proper injection time

!
!"#
[4]
:

!
!"#
=
!

ln

(
1
+
!
!"#
!
!
!
!
!
!
!"#
!
!
)
,

where,
!
!
=
0
.
5
(
!
/
!
)
!
!
,
!
=
!
!
!
!
!

is the cavity time constant. It should be noted that the
pre
-
detuning for synchronous phase and frequency tracking at filling stage are already
applied. Figure 4 shows
that there is significant impr

beam

injection time.

When beam injection time cannot be adjusted in some cases such as in beam commission
,

where a variety of beam modes expect to pass through the cavity with different pulse
length
s
, peak current
s
, and arrival

time
s
, the way to improve field stability is to apply
individual feedforward compensation for each beam mode. Figure 5 and Figure 6 show
respectively the cavity fields and consumed powers for the cases without/with individual
feedforward for each beam mod
e.

More
results not shown here indicate

that even if there are errors in feedforward signal
such as beam current fluctuation and droop, and beam arrival time jitters, the cavity field
can be kept well.
However, better performance is achieved when arri
val time jitter is less
than 100ns.

Figure
3

C
avity field and generator power consumed under PI feedback control

for nominal beam operation (beam injected 200us after
constant cavity field is built)

Figure
4

Cavity field improvement by adjusting properly beam injection time

for nominal beam operation

(PI feedback has been applied)

Figure
5

Cavity field and power consumed under PI feedback for different beam modes loading

Figure
6

Cavity field improvement by individual feedforward compensation for each beam mode

been applied)

0
1
2
3
4
5
x 10
ï
3
0
5
10
15
20
25
Amplitude / MV
Time / s
Cavity Field
0
0.5
1
1.5
2
2.5
3
x 10
ï
3
ï
8
ï
6
ï
4
ï
2
0
2
4
6
Phase / deg.
Time / s
Cavity Field
0
1
2
3
4
5
x 10
ï
3
0
0.5
1
1.5
2
2.5
Time / s
Power / MW
Forward and Reflected Powers

forward power
reflected power
0
1
2
3
4
5
x 10
ï
3
0
5
10
15
20
25
Amplitude / MV
Time / s
Cavity Field
0
0.5
1
1.5
2
2.5
x 10
ï
3
ï
10
ï
8
ï
6
ï
4
ï
2
0
2
4
6
Phase / deg.
Time / s
Cavity Field
0
1
2
3
4
5
x 10
ï
3
0
0.5
1
1.5
2
2.5
Time / s
Power / MW
Forward and Reflected Powers

forward power
reflected power
0
1
2
3
4
5
x 10
ï
3
0
5
10
15
20
25
Amplitude / MV
Time / s
Cavity Field

1st, 12.5mA, 100us
2nd, 25mA, 100us
3rd, 50mA, 100us
0.5
1
1.5
2
2.5
x 10
ï
3
ï
8
ï
6
ï
4
ï
2
0
2
4
6
Phase / deg.
Time / s
Cavity Field

1st, 12.5mA, 100us
2nd, 25mA, 100us
3rd, 50mA, 100us
0
1
2
3
4
5
x 10
ï
3
0
0.5
1
1.5
2
2.5
Time / s
Power / MW
Forward and Reflected Powers

1st, forward
2nd, forward
3rd, forward
1st, reflected
2nd, reflected
3rd, reflected
0
1
2
3
4
5
x 10
ï
3
0
5
10
15
20
25
Amplitude / MV
Time / s
Cavity Field

1st, 12.5mA, 100us
2nd, 25mA, 100us
3rd, 50mA, 100us
0
0.5
1
1.5
2
2.5
3
x 10
ï
3
ï
20
ï
10
0
10
20
30
Phase / deg.
Time / s
Cavity Field

1st, 12.5mA, 100us
2nd, 25mA, 100us
3rd, 50mA, 100us
0
1
2
3
4
5
x 10
ï
3
0
0.5
1
1.5
2
2.5
Time / s
Power / MW
Forward and Reflected Powers

1st, forward
2nd, forward
3rd, forward
1st, reflected
2nd, reflected
3rd, reflected
Reference

[1
] H. Padamsee, RF Superconductivity: Science, Technology, and Applications, Wiley, New
York,

2009.

[2] T. Schilcher. Vector Sum Control of Pulsed Accelerating Fields in
Lorentz

Force Detuned Superconducting Cavities. Ph. D. Thesis of DESY, 1998

[3] R. Zeng,
Power Overhead Reduction Considerations for RF Field Control in
Beam
Commissioning
, ESS technotes, ESS
-
doc
-
263
-
v1.

[
4
]
R. Zeng, S. Molloy, Some Considerations on Predetuning for Superconducting Cavity, ESS
technotes,