Fundamental Concepts of Particle Accelerators IV: RF ...

.

.

. ..

.

.

Fundamental Concepts of Particle AcceleratorsIV: RF Technology

Koji TAKATA

KEK

[email protected]://research.kek.jp/people/takata/home.html

Accelerator Course, Sokendai

Second Term, JFY2013

Oct. 24, 2013

Contents

§1 Dawn of Particle Accelerator Technology

§2 High-Energy Beam Dynamics (1)

§3 High-Beam Dynamics (2)

§4 RF Technology

• Accelerating Cavities

• High Voltage Breakdown

• RF and Superconductivity

• Klystron

§5 Future of the High Energy Accelerators

§6 References

Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 2 / 1

Accelerating Cavities (1)

Classification

Single cell structure

• Single acceleration gap

• Multiple acceleration gaps

Multicell Structure

• Traveling wave (TW) structure

• Standing wave (SW) structure



Single cell structure with single acceleration gap: typical example

Cavity for the KEK Photon Factory ring

fRF = 500MHz (λ/2 = 300mm)

R234.69mm

R91.375mmR50mm

220mm

300mm

R130mm

R10mm

Ez (r=0)

z

r



Single-cell structure with a single acceleration-gap: for proton synchrotrons

Resonance frequency modulation is essential for proton synchrotrons,since the proton’s velocity continuously increases with acceleration.

The cavity below is used at the J-PARC proton synchrotrons:• Six discs (red) are made of a magnetic-alloy tape of high permeability µ

• Modulate µ by bias-currents → fres ∼ 1MHz → 2MHz

φ

magnetic-alloy discs

acceleration gap

beam

ceramic pipe

600 mm

247 mm



Single-cell structure with multiple acceleration gaps: typical example

Drift tube linac (DTL) for the proton linac in the J-PARC

fRF = 324MHz (λ = 926mm)

proton’s β : 0.08 (3MeV) → 0.56 (190MeV)



Single-cell structure with multiple acceleration gaps: typical example

• Drift tube linac (DTL) for the proton linac in the J-PARC



Multicell structure with multiple acceleration gaps:

• disk-loaded structure (DLS)

• Typical traveling wave structure for electron linacsa cut-away view

fRF = 2856MHz (λ = 105mm), cell length λ/3 = 105mm (the 2π/3 structure)



Multicell structure with multiple acceleration gaps: standing wave linac

Alternating Periodic Structure: APS

fRF = 2856MHz (λ = 105mm), cell length λ/3 = 105mm (the 2π/3 structure)



Multicell structure with multiple acceleration gaps: standing wave linac

side-coupled structure

E. A. Knapp, ”High Energy Structures” in Linear Accelerators,

ed. P. M. Lapostolle and A. L. Septier, p. 607 (North-Holland, 1970).


High Voltage Breakdown (1)

1 Fowler-Nordheim theory of the field emission (dark currents)

2 Kilpatrick criterion

3 Surface damages on the cavity surface

4 Superconductivity and RF



Fowler-Nordheim’s Theory of Field Emission (1)

R. H. Fowler and L. Nordheim, Proc. Roy. Soc. A 119 (1928) 173

Current density jF [A/m2] of the field emission from metal surfacedue to the static electric field gradient E [V/m]:

jF =1.54× 10−6 × 104.52ϕ

−0.5(βE)2

ϕexp

(−6.53× 109ϕ1.5

βE

)Work function: ϕ [eV]

Macroscopic surface gradient: E [V/m]

Effective gradient with a multiplication factor β due to surfaceroughness: βE

β is usually called the field enhancement factor.

By conditioning, β gradually shrinks from 102∼3 to ∼ 101 for purecopper.




Modified expression for RF fields:J. W. Wang and G. A. Loew, SLAC-PUB-7684 (1997)

Substituting E sinϕ for E in the formula for the static field andaveraging the current over an RF cycle:

(1/2π)

∫ 2π

0jF dϕ,

we obtain the following fairly good approximation for the RF field:

jF =5.7× 10−12 × 104.52ϕ

−0.5E2.5

ϕ1.75exp

(−6.53× 109ϕ1.5

E

)



Kilpatrick Criterion W. D. Kilpatrick, Rev. Sci. I nstr. 28 (1957) 824

Parallel metallic plates: gap spacing g, peak applied voltage V , maximum ionenergy W , and surface field gradient E = V/g.

Electron surface emission (next slide) is proportional to jF = E2 exp(−k/E), withk some constant for the cathode material.

Secondary electron emission jF2 by positive ions, the number of which isproportional to jF , seems proportional to the ion’s energy W .

Hence breakdown would occur when jF2 > jF and, otherwise, no breakdown.

For many experimental data, he obtained a good fitting for the critical conditionjF2 = jF as shown below.


High Voltage Breakdown (5): Disrupted Surface of a Copper Cavity

Disk loaded structure for an X band linac after high voltageconditioning at around several tens of MV/m RF fields.

f = 11.4GHz (λ = 2.63 cm)

R. E. Kirby, SLAC-PEL, 2000


Superconductivity and RF (1)

At extremely low temperatures, copper’s resistivity decreases to10−2∼−3 of the room temperature value, and the cavity wall loss toodecreases in the same way. But if we consider the cryogenic power tokeep the cavity extremely cold, the total electric power ratherincreases.

However the resistivity of superconductors would be less than ∼ 10−9

of the room temperature resistivity of copper. Therefore developmentof superconducting cavities has been continued since 1960s usingniobium (Nb) in particular.

The first acceleration was accomplished with a superconductingelectron linac at Stanford University in 1977.


Superconductivity and RF (2): Critical Magnetic Fields of Nb

Temperature dependence of the critical fields

• H < Hc1: Meissner state (perfect superconducting state)• Hc1 < H < Hc2: mixing of superconducting state and normalconducting state

• Hc2 < H: normal conducting state

∗ †

∗K. Saito: srf2003.desy.de/fap/paper/MoO02.pdf†1Gauss = 1× 10−4Tesla, 1Oersted = 1000/(4π)A/m


Superconductivity and RF (3):

Nb’s Resistivity around Critical Temperature Tc∗

RRR (residual resistance ratio) is the ratio of room temperatureresistivity over that of T = 0 and a measure of the purity of metals.

∗W. Singer et al : TTC-Report 2010-02 (DESY)Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 18 / 1


Basic properties of superconducting niobium (Nb)

For high-purity Nb:

• Critical temperature: Tc = 9.2K

• Critical magnetic field: Hc = 2× 103Oe

• Meissner state for H ≤ Hc1 = 1.7× 103Oe at T = 0K

• Normal state for H ≥ Hc2 = 2.3× 103Oe

• Coherent length ξ0: ∼ 40 nm at T = 0K

Electric field due to magnetic induction accelerates

both normal and superconducting electrons.

• Normal conducting currents induce ohmic losses.

• Hence the cavity Q value is not infinite but on the order of

several times 109, which is about 105 times larger than that of

typical copper cavities.



Q0 Values of a 1.3GHz Nb Cavity ∗

∗Kenji Saito (2008)Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 20 / 1


Electromagnetic fields inside the surface of superconductors

Maxwell equations:

∇×E+ µ∂H

∂t= 0, ∇×H− ε

∂E

∂t= J (= Js + Jn) , Jn = σnE,

where σn is the conductivity in the normal state.

London equations:

Js = −jnse

2

ωmeE, ∇× Js = −nse

2

meµH.

Field equations satisfying the above two sets of equations:

∇2 (J,E,H) =(λ−2L + jωσnµ− ω2εµ

)(J,E,H)

≈(λ−2L + jωσnµ

)(J,E,H) ,

where λL =√

me/nse2µ: London’s penetration depth,

which is about 50 nm for Nb.∗∗For Nb, µ can be set at µ0.


Superconductivity and RF (7): Surface Resistance of Metal Wall

Surface impedance Zs is given by

Zs = E∥/H∥,

where ∥ means the components parallel to the surface.†

RF power loss Pwall depends on the real part of the surface impedance

Rs = Re[Zs]

and is given by Pwall/per unit area =1

2Rs

∣∣H∥∣∣2

.For superconductors, σs (≡ 1/µωλ2L) ≫ σn and hence

Rsupers ≈ 1

2σnω

2µ2λ3L

For normal conductors, σs = 0 and hence

Rnormals ≈

√ωµ/2σn (= 8.5mΩ for Cu)

Actual values for superconducting Nb (2K) and Cu (300K) atω/2π = 1GHz:

Rsupers . 2× 10−6 Rnormal

s = 17nΩ

†In vacuum Zs = Z0 = 377Ω .Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 22 / 1

Klystron (1)

UHF RF power source for the KEKB collider

Frequency: 508MHz, Power output: 1MW CW.


Klystron (2)

Schematic diagram of the klystron cross-section


Fundamental Concepts of Particle Accelerators IV: RF ...

Documents

Transcript of Fundamental Concepts of Particle Accelerators IV: RF ...