p and 0 mode interaction in rf gun john schmerge, slac november 3, 2004

November 3, 2004 John Schmerge, SLACInjector RF Design Review [email protected]

and 0 Mode Interaction in RF Gun John Schmerge, SLAC

November 3, 2004

LCLS 1.6 Cell Gun 2 resonant frequencies2 resonant frequencies Bead drop resultsBead drop results Full and half cell field probesFull and half cell field probes

Measurements Time Domain Time Domain Frequency Domain Frequency Domain

Calculations No pulse shaping No pulse shaping With pulse shaping With pulse shaping

Summary


Multiple Modes2 modes with different resonant frequencies and different longitudinal field profiles.

ff – f – f00 = 3.5 MHz on GTF gun = 3.5 MHz on GTF gun

Beating observed during gun filling time (transient effect)Beating observed during gun filling time (transient effect)

Presence of 0 mode affects e-beamTime dependent ratio of full cell to half cell field due to the 180˚ Time dependent ratio of full cell to half cell field due to the 180˚ phase shift between the two modes affects longitudinal phase phase shift between the two modes affects longitudinal phase space.space.

Additional transverse fields in the cell-cell aperture affect Additional transverse fields in the cell-cell aperture affect transverse phase space.transverse phase space.

Measure each modeMeasure in time or frequency at a particular longitudinal position Measure in time or frequency at a particular longitudinal position (RF probes).(RF probes).

Measure as a function of longitudinal position averaged over time Measure as a function of longitudinal position averaged over time (bead drop).(bead drop).


Bead Drop Measurement

-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

0 20 40 60 80 100

Bead End Position (mm)

Fre

quen

cy S

hift

(kH

z)

SF sim, pi-modepi-mode measSF sim, 0-mode0-mode meas

0-mode

-mode


Scale2" 3"0 1"

Laser Port

RF Probe Location on GTF Gun

Scale2" 3"0 1"

Half Cell Probe

Full Cell Probe

Waveguide Feed


Time Domain Measurement

Temporal Response with ≈ 6 MW incident powerEcathode ≈ 90 MV/m

0123456789

10

0 1 2 3 4

Time (ms)

Po

we

r (M

W)

0102030405060708090100

Fie

ld (

MV

/m)

ForwardReflected

Full CellHalf Cell

-90

-70

-50

-30

-10

10

30

50

70

90

0 1 2 3 4

Time (ms)

Ph

ase

(°)

ForwardReflected

Full CellHalf Cell


Time Domain Measurement

Temporal Response with ≈ 6 MW incident powerEcathode ≈ 90 MV/m

0

1

2

3

4

5

6

7

8

0 1 2 3 4

Time (ms)

Po

we

r (M

W)

-12%

-9%

-6%

-3%

0%

3%

6%

9%

12%

Efu

ll -

Eh

alf (

MV

/m)

Forward

Full - Half Cell


0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

2850 2852 2854 2856 2858

Frequency (MHz)

Mag

nit

ud

e

p mode0 modeTotalMeasured

-3.15

-1.58

0.00

1.58

3.15

2850 2852 2854 2856 2858

Frequency (MHz)

Ph

ase

(rad

ian

s)


0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

2850 2852 2854 2856 2858

Frequency (MHz)

Mag

nit

ud

e


-3.15

-1.58

0.00

1.58

3.15

2850 2852 2854 2856 2858

Frequency (MHz)

Ph

ase

(rad

ian

s)


Frequency Domain Measurements

Full Cell Probe Half Cell Probe


-8.0E-03

-4.0E-03

0.0E+00

4.0E-03

8.0E-03

-8.0E-03 -4.0E-03 0.0E+00 4.0E-03 8.0E-03

Real

Imag

inar

y

Measured

Calculated

-8.0E-03

-4.0E-03

0.0E+00

4.0E-03

8.0E-03

-8.0E-03 -4.0E-03 0.0E+00 4.0E-03 8.0E-03

Real

Imag

inar

y

Measured

Calculated

Transfer Function Vout/Vin

Full Cell Probe Half Cell Probe

mode

Sum (full cell) or difference (half cell) of two second order band pass filters


Output Response Equations

22

2out out in

outL L

d V dV A dVV

dt Q dt Q dt

4 3 2 2 22 2 2 20 0 0 0

0 04 3 20 0 0

out out out outout

L L L L L L

d V d V d V dVV

dt Q Q dt Q Q dt Q Q dt

mode only

and 0 mode

3 2 2 20 0 0 0 0 0

3 20 0 0

in in in

L L L L L L

A A d V d V A A dV

Q Q dt Q Q dt Q Q dt


GTF Measurements and Fits from 1998

Gun RF vs Time

0

2

4

6

8

10

12

-2.50 -1.50 -0.50 0.50 1.50 2.50

Time (ms)

Po

wer

(M

W)

-100

-50

0

50

100

150

200

Ph

ase

(deg

rees

)

gun forward

gun field

gun reflected

Gun field (calculated)

gun reflected (calculated)

gun forward phase

t = 391 nsb = 0.98df = -76 kHzT = 42 C

Gun RF vs Time

0

2

4

6

8

10

12

-2.50 -1.50 -0.50 0.50 1.50 2.50

Time (ms)

Po

wer

(M

W)

-100

-50

0

50

100

150

200

Ph

ase

(deg

rees

)

gun forward

gun field

gun reflected

Gun field (calculated)

gun reflected (calculated)

gun forward phase

t = 884 nsb = 0.98df = -62 kHzT = 42 C

Fit Gun Field Waveform Fit Reflected Power Waveform


Step Function Response

0

0 0

0 0 0

( ) cos cos

cos cos

RF RF

t t

V t A t A t

B e t B e t

t t

Steady state response at applied frequency

Transient response at resonant frequencies


Transient Response Including 0 Mode

f = 2856.00 MHzf = 2856.03 MHzf0 = 2852.53 MHzQ0 = 12000Q0 0 = 12000b = 1.3b0 = 0.7t = 576 nst0 = 779 ns


GTF LCLS

0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-14%

-10%

-6%

-2%

2%

6%

10%

14%

(Efu

ll -

Eh

alf)/

Em

ax (

%)

EfullEhalfEnomEfull - Ehalf

0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-14%

-10%

-6%

-2%

2%

6%

10%

14%

(Efu

ll -

Eh

alf)/

Em

ax (

%)

EfullEhalfEnomEfull - Ehalf


Transient Response With Pulse Shaping



GTF LCLS

0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-21%

-15%

-9%

-3%

3%

9%

15%

21%

(Efu

ll -

Eh

alf)/

Em

ax

(%)Efull

EhalfEnomEfull - Ehalf

0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-21%

-15%

-9%

-3%

3%

9%

15%

21%

(Efu

ll -

Eh

alf)/

Em

ax

(%)Efull



Transient Response With Pulse Shaping



LCLSAdjusted timing

LCLSIncreased f

0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-21%

-15%

-9%

-3%

3%

9%

15%

21%

(Efu

ll -

Eh

alf)/

Em

ax

(%)Efull


0

20

40

60

80

100

120

140

0 1 2 3 4

Time (ms)

E (

MV

/m)

-21%

-15%

-9%

-3%

3%

9%

15%

21%

(Efu

ll -

Eh

alf)/

Em

ax

(%)Efull



Frequency Domain

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

2850 2852 2854 2856 2858

Frequency (MHz)

Mag

nit

ud

e

Input

Gun

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

2850 2852 2854 2856 2858

Frequency (MHz)M

agn

itu

de

Input

Gun

Flat klystron pulse (3 ms) With pulse shaping (0.56 ms)


Summary0 mode produces a measurable 3.5 MHz beating on the gun field

Effect more significant with short pulses used for rf pulse shapingEffect more significant with short pulses used for rf pulse shaping

Estimated time dependent full cell to half cell field ratio varies by Estimated time dependent full cell to half cell field ratio varies by less than 10% and for special cases less than 2%.less than 10% and for special cases less than 2%.

Effect depends on the filling time (coupling coefficient), mode Effect depends on the filling time (coupling coefficient), mode separation and exact input waveform. Timing can be adjusted to separation and exact input waveform. Timing can be adjusted to minimize beating.minimize beating.

Mode beating can be advantageous as it allows for variable field balance depending on laser timingShot to shot jitter on the beating will be dominated by fluctuations on the klystron input pulse.Measure beating at GTF with rf pulse shaping.

p and 0 mode interaction in rf gun john schmerge, slac november 3, 2004

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