Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010

Linac RF System

A. Nassiri -ANL

2

Outline:

Linac Layout

Power system

Klystron Operation

RF Components

RF Breakdown and RF Conditioning

Measurement Techniques

Some Examples

3

Linac RF Layout

L1L2 ACS2L2 ACS3 L2 ACS1L2 ACS4

Bunch Compression

DIADIA

L2

DIA

AML4 ACS1L4 ACS2L4 ACS3L4 ACS4L5 ACS1L5 ACS2L5 ACS3L5 ACS4

L4L5

4

Water Station

KLYMod Cab 1Mod Cab 2Mod

Cab3

LLRF

VAC VAC

Coupler

Coupler

SLED

3dB Hybrid 3dB Hybrid

3dB Hybrid

5

AC Line

PSAC DC

EnergyStoringElement

Switch

1:n

Pulsed Transformer

Klystron

40 KVDC0.75 ACC EMIPower Supply

PFN40 KVDC5 µsec

Thyratron

Linac Modulator System

Steel Core

Primary Winding

Secondary Winding

6

A B C3-phaseAC power

GND

PFN-V

DumpSwitch

HV

ChargingSupply Rev Protection

CircuitCuPlate

40 KVDC PFN

2x8 cellsEOL

KLY

RF Power

1:15.3

Safety

PrimVolt

HeaterDriver

APS Linac Modulator 300 kV/300 A

20 KVPulse

7

8

9

S-Band 35 MW Klystron

10

Klystron/SLED Unit WG Coupler at the output of the klystron

SLED Housing

Klystron Collector

56dB coupler

11

Velocity Modulation

Velocity entering, uo

Velocity leaving, uo+∆u

d

t=to, z=0

visinωt

When electrons are passed through the modulating field, some electrons have their velocities increased and some will have their velocities decreases when the voltage is reversed.

As the electrons leave the gap, those with increased velocities overtake the slower electrons, as a result electron bunching (density modulation) occurs.

12

0 30 60 90 120

Drive Power [W]

5

10

20

30 30 kV

25 kV

20 kV

10 kV

Typical Klystron Saturation Curves

Operating Bandwidth

fo

f2 f1 f5 f3 f4

Cavity Bandwidth

13

Breakdown and Protection

• In the gun (between electrodes,between leads or from electrodes or leads to ground)

• In the collector

• In high-power portion of the RF structure

14

RF Components:

• Driver amplifier to power klystron

• Klystron is used to generate high peak power ( A small accelerator)

• Need to transport power to the accelerating structure

• Waveguide is used (under vacuum) to propagate and guide electromagnetic fields

• Windows (dielectric material, low loss ceramic) are used to isolate sections of the waveguide

• Termination loads (water loads) are used to provide proper rf match

and to absorb wasted power• Power splitters are used to divide power in different branches of the

waveguide run

15

Rectangular Waveguide

a

bacfc 2

=

For S-band:

GHzcmcmf

cma

c 875.116

sec/103 8

10

=×

=

=

Cut-off frequency:

16

A

B

C D

Top View

Side View

End View

Voltage Traveling Wave

17

Guide Wavelength:

cm

GHzGHz

cmGHzf

ff

g

c

c

g

5.18

856.2 875.11

5.10, 875.1 Using

1

2

2

=

−

=

=

−

=

λ

λλ

18

x

y

za

b

Waveguide Propagation Modes

TE - Transverse Electric Field

TM - Transverse Magnetic Field

E-fieldH-field

( )

evanescentimaginaryeg propagatinreal

f

c

cc

mod e mod

2 , 2

2 2

2122

0

00

⇒≡⇒≡−=

==

===

ββ

κκβ

λπκ

λπκ

λπ

νπ

νωκ

19

RF Components:

• Power dividers are 4-port hybrids of various coupling(I. E. a 3-dB hybrid splits the input power in half)

Input Power, Pin

Matched Load

Aperture Coupling

Output Power, =1/2PinPout

Output Power, =1/2PinPout

20

RF Components:

Couplers Window

21

TE015

CylindricalStorage Cavity

Input power

Output power

3 dB

Hybrid

SLED

22

SLED Operation Incident Wave

Reflection Wave

Incident Wave

Reflection Wave

Emitted Wave

Propagated Wave

inE

inE

−

eE

propE

outE

ineout EEE

−= π-shift ineout EEE

+=

23β

κωω

βκ

β

κκ

200

2

)(

2

2

Coeff. Coupling

)(

ecc

ec

dissc

e

ineout

inin

ccoutin

EQPQU

EP

PP

EEPEP

dtdUPPP

==

=

=

Γ+=

=

++=

24

dtdEEQEEEEEE

dtdEEQEEEE

EUt

dtdEEQ

dtdU

eeeineinein

eeeinein

e

c

ee

e

ωββ

ωββ

π

ωβκ

02222

0222

0

212

21)(

1set shift, phase for account To0

0,0At

2

++−+=

++−=

−=Γ=∴

==

=

25β

ωβωωββ

ωββ

ωββ

ωββ

+==+

+−+=

++−=

++−=

++−+=

1 ,

2

22)11(0

121210

2120

212

0

0

0

0

022

02222

QQEQ

EQdt

dEdt

dEQEE

dtdE

EQ

EE

dtdEEQEEEE

dtdEEQEEEEEE

LineL

e

eee

e

ee

in

eeeinee

eeeineinein

26

≤−≤

=

=+

+==

ttttttt

E

EEdt

dET

QT

in

inee

c

Lc

2

21

1

.

,0 ,1

0 ,1

: 12 and 2 Defining

end the towardsreversal phase with pulse amplitudeconstant a is SLED theInput to

α

ββα

ω

0 t1 t2

1

-1t

27

3.5

3.2sec68.2

sec82.0 sec,86.1 ,sec5.3

16667 6

5101

0

66.16

1012

:numbers Typical1)1()(

2max

max

1

WidthPulseKlystron 2

1max

1

≈∝

≈=

==≈

=⇒=+

=

==+

=

+−===−

EPEt

TcTt

LQQ

LQ

ettEE

f

Tt

outc

µ

µµµβ

ββα

α

28

5

4

3

2

1

2

1

0

-1 0 1 2 3 4t (µsec)

0 1 2 3 4 t (µsec)

Field

PowerPin

Pout

Ein

Eout

Ee

29

SLED

30

SLED UNIT

High Q storage cavities

TM015 Mode

3dB hybrid

Input power

Output power

31

Disk-Loaded Constant Gradient S-Band Structure

32

Accelerating Structure

λ0

2π/3 phase shift per cell

33

3-meters S-band Structure Input coupling cell

Input coupler

Cells with tuning nut

34

35

W-Band (94 GHz) Accelerating Structure

36

How to Accelerate?

Evqdtd

•=ε

tkvdtE ) - cos( 0

ωε ∫=∆

- +E

dB/dt

E

B

E100 MV

102 MV105+? MV

Injection Linac

v<c v≈c

37

fr =

c = λ/T = λ × 1/T = f λ

Propagation Fields E-field

H-field

xy

z

Time

LCπ21

38

Time of one period, T

Distance of one wavelength, λ

E field H field

Direction of propagation

39

Voltage Standing-Wave-Ratio VSWR

VSWR is defined as the ratio of Emax : Emin

Emax = Vi + Vr = Vi (1+P)

Emin = Vi - Vr = Vi (1-P)

VSWR, S = Emax / Emin =

If p=0 (matched line), S=1

If p=1 (open or short-circuited line, S = ∞

PP

−+

11

40

Example 1:A 400 W amplifier is used to drive the input cavity of the linac klystron. Lets assume that for the HV setting of 300 kV and 290 A, a klystron required 120 W to provide 25 MW of rf power. Suppose that input drive power is transmitted down a 50-Ω loss-free line and is terminated at the input cavity of the klystron which presents a 42- Ω load to the generator.

1) what is the reflected power going back to the generator?

2) What is the excitation power into the 1st cavity of the klystron

VSWR, S =

Reflection coefficient,

Reflected Power, Pr = P2 × Pi = (0.087)2 × 120 W = 0.90 W

Transmitted power to klystron, PL = Pi - Pr = 120 - 0.9 = 119.1 W

19.142500 ==

LRZ

087.019.219.0

11

==+−

=SSP

41

Example 2:L1 klystron is set to generate 23 MW, measured at the klystron output coupler. The waveguide run from L1 klystron to the input of the ACS1 is roughly 75 feet. Assume that there are two windows in this run, each with a 0.12 dB loss. WR-284 waveguide has a 0.45 dB loss/100 ft. There are 12 flanges in between each with a 0.07 dB loss.

1) what is VSWR for each component?

2) what is the reflected power at the klystron?

3) what is the forward power to the ACS1?

42

SdBloss 10log20)( =

03.110log1012.0:

012.010 ==⇒= SSdB

Windowloss

016.110log1007.0:

007.010 ==⇒= SSdB

Flangeloss

dBftftdB

ossWaveguidel

34.01007545.0

:

=×

43

1.110log1034.0:

034.010 ==⇒= SSdB

Waveguide

dBdBdbdB 3.134.01207.0212.0 Waveguide(12) Flanges (2) Windows

:loss Total

=+×+×++

44

MWMWMWPMWMWPP

PP dB.-

window

rr

r

r

6.14.464.4674.074.

log1031

:indowklystron w at thepower Reflected

12

1

210

=−==×==

=

MWMWMWPPPMWMWPP

PPdB

PPdB

tincrefl

inct

inc

t

inc

t

61723172374.074.0

log103.1

log20)( loss Total

10

10

=−=−==×==

=−

=

45

How does one measure rf power?

• Cannot measure high peak power with any power instruments

• Need to sample a portion of the peak power so a peak powermeter can be used without damage

• A waveguide coupler inserted in-line with waveguide is used for this measurement• Coupling loops are used to sample a small portion of the peakpower• A typical forward loop coupling factor is -56 dB

• For a 30 MW peak power, this corresponds to ~75 W (SAFE)

• Attenuation elements can also be added to reduce the peak power for measurement purposes

46

Some Basic RF Parameters

1. The shunt impedance per unit length is a measure of excellence of a structure as an accelerator

Higher shunt impedance is desired since it means more accelerating field for a given spent power.

2. The “unloaded” Q-factor is a measure of the merit of rf cavity as a resonator.

dzdpEr z

/

2

0−

=

dzdpwQ

/

0ω−

=

47

3. The ratio of is a very basic parameter in microwavecavities and structures.

00 / Qr

wEQr z

/ 0

2

00 ω=

20

2

02 sec -

−×∝

×∝

ωz

z

Ewor

areationalcrossEw

ω∝00 / Qr

48

4. Group velocity, , is the velocity at which rf energy

flows through the accelerator. It strongly depends on the

ratio of disk aperture diameter (2a) to cavity diameter (2b):

is an important parameter:

4.1. The fill time, time that is required to fill the accelerator with rf energy depends upon group velocity

gv

4)( baKcvg ≈

gv

gvl

ft =

49

4.2. The power flow into the structure and the energy stored perunit length of the structure are interrelated to

Since , lower value of group velocity is preferred fromthe point of view of obtaining maximum accelerating fields for a given power flow.

4.3 In general, decreasing , results in increasing anddecreasing Q0 which results in increasing

gvgv

Pw =

zEw 02∝

gv 0r00 / Qr

50

Phase velocity - is the velocity of light (plane wave) in the evacuated waveguide.

This is greater than the speed of light at which the particles travel.

Need to slow down the phase velocity inside the structure so that it is synchronous with particle velocity.

µεκω

βω 1== pv

51

Example: A simple “back-of-the-envelop” calculation

L4 klystron is setup with 290 kV and 270 A on the modulator. L4 klystron has an efficiency of 42%. What the output power of the L4 klystron? What is the output power of the SLED? If the rf pulse length of the driver amplifier is set to 4 µsec, what is the rf pulse length of the SLED output? How long does it take to fill the SLED? What is the power level at each accelerator structure? Assume 7% loss at each power split. If the klystron and the structure are operating at 30 Hz, what is the average power dissipated in the klystron and the structure?

52

sec86.1102856 6

102)1(

2sec 2length pulse rf SLED

5.1341.48.32)(

8.3242.03.78)(3.78270290

6

50 µ

πωβ

µ

=×××

×=

+=

≈

=×=

=×==×=

Qt

MWMWSLEDPMWMWklyP

MWAkVP

fill

rf

rf

DC

53

After the first split, output power is 125.1/2 = 62.55 MW. After the second split, output power of each feed is 58.17/2 = 29 MW. So each structure receives ~29 MW rf power.

kWMWstructureP

kW

MWklyP

avg

avg

74.1

sec 2 pps 3029)(4

sec104 pps 3010 32.8

sec 4 pps 308.32)(66

=

××=≈

××××=

××=−

µ

µ

54

Example:Each RF gun in the linac needs approximately 5 MW to provide a beam energy of about 1.6 MeV for injection into the linac. If the output power of L1 klystron is 23 MW, what is the maximum rf power available to each gun?

55 8.823

48.0 2856 2

meters 3000,14

0065.0 - 0204.0

2

48.02

2

MWeMWP

MHzlQ

cv

Qvl

ePP

out

g

g

in

out

=×=

≈×=

==

=

=

=

×−

−

τπω

ωτ

τ

56

Forward Coupling Coupling, forward

-20 dB0.01 mW

-0.046 dBm

0.99 mW

Coupling Factor (dB) =incident

forward

PP

log10−

ZoSource

0 dBm1 mW

57

ZoSource

0 dBm1 mW

-0.046 dBm

0.99 mW

Coupling, reverse-50 dBm0.00001 mW (10 nW)

incident

reverse

PPlog10−Isolation Factor (dB) =

Directional Coupler Isolation

58

Directional Coupler Directivity

(dB) Loss-Factor(db) Coupling-dB)Isolation( (dB)y Directivit

IsolationLossFactor Coupling

y Directivit(reverse)

arm)(through (fwd)

=

×=

50 dB 20 dB

Directivity = 50 dB - 20 dB = 30 dB

59

Handy Formulas

For a constant-gradient structure:

τω

α

ωααωτ

τ

Qt

lePconstz

dzdP

Qzvl

Qzvl

f

in

gg

2

)1()(2

)(2,

)(22

=

−==−=

===

−

Fill time:

60

Handy Formulas The energy gain of a charged particle is Ε

21

21

)](/)1[()2( rlPe inττ τ−−=Ε

MeVE

MeVE

mmMMWeE

QmeterMr

56structure, theinput toMW 32or Fstructuremeter -3in 47

)3 /5423)(48.0

1()48.02(

48.014000

/54

5.048.0

5.0

≈

≈

×Ω×−

×=

==

Ω=

−

τ

61

Handy Formulas

Structure efficiency:

SuppliedEnergy Energy Stored

=η

τη

τ

21 2−−

==e

tPW

fin

65.048.0238.01

=×−

=η

62

63

64

Breakdown depends on: The applied field level and local field enhancement

The breakdown field of the medium (gas,Vacuum,solid)

Gas ~10’s V/cm - 10 kV/cm (depends on pressure and type)

Vacuum ~ 0.5 - 1MV/cm

Types:

- DC Breakdown in Gas

- DC Breakdown in Vacuum

- RF Breakdown in Gas

- RF Breakdown in Vacuum

65

RF Breakdown in Gas: DC breakdown field for air at atmospheric pressure is about 30 kV/m

RF breakdown field depends on the frequency, spacing and pressure

66

RF Breakdown in Vacuum:1. Kilpatrick’s criterion: Relates max. field Ek[MV/m] at any frequency f[Hz];

Very often, however, another king of discharge develops at voltage levels well below the Kilpatrick level. This discharge is called Multipactor Discharge.

Multipacting occurs when electrons move back and forth across a gap in synchronism with an rf field. If the secondary emission ratio of the gap surface is greater than unity, then the number of electrons involved in the process build up with time and electron avalanche will be initiated and sparking might result.

)/5.8exp(1064.1 26kk EEf −×=

n=1 n=2 n=3

67

RF Conditioning with short Pulse: