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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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 3 / 1
Accelerating Cavities (2)
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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 4 / 1
Accelerating Cavities (3)
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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 5 / 1
Accelerating Cavities (4)
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)
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 6 / 1
Accelerating Cavities (5)
Single-cell structure with multiple acceleration gaps: typical example
• Drift tube linac (DTL) for the proton linac in the J-PARC
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 7 / 1
Accelerating Cavities (6)
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)
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 8 / 1
Accelerating Cavities (7)
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)
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 9 / 1
Accelerating Cavities (8)
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).
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 10 / 1
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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 11 / 1
High Voltage Breakdown (2)
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 12 / 1
Fowler-Nordheim’s Theory of Field Emission (3)
Fowler-Nordheim’s Theory of Field Emission (2)
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
)
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 13 / 1
High Voltage Breakdown (4)
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 14 / 1
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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 15 / 1
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 16 / 1
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
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 17 / 1
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
Superconductivity and RF (4)
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 19 / 1
Superconductivity and RF (5)
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
Superconductivity and RF (6)
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 21 / 1
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.
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 23 / 1
Klystron (2)
Schematic diagram of the klystron cross-section
Koji Takata (KEK) Fund. Conc. Part. Acc. 4 Acc. Course, Oct. 2013 24 / 1