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Radio Frequency Radio Frequency QuadrupoleQuadrupoleAlessandra LombardiAlessandra Lombardi
RFQ CAS 2005 , Zeegse, 26 may 2005
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Radio Frequency Radio Frequency QuadrupoleQuadrupole is on is on the school poster!the school poster!
CERN RFQ1
520 keVprotons
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ContentsContents
Motivation and historical introductionMotivation and historical introduction
What is a radio frequency What is a radio frequency quadrupolequadrupole(RFQ) ?(RFQ) ?
Designing a RFQDesigning a RFQ
Frequently asked questions Frequently asked questions
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RFQ history RFQ history 1970 1970 KapchinskijKapchinskij and and TeplyakovTeplyakov propose the idea of the propose the idea of the radiofrequency radiofrequency quadrupolequadrupole ( I. M. ( I. M. KapchinskiiKapchinskii and V. A. and V. A. TeplvakovTeplvakov, , Prib.TekhPrib.Tekh. . EkspEksp. No. 2, 19 (1970)). No. 2, 19 (1970))..1974 experimental test of K&T idea at USSR Institute for H1974 experimental test of K&T idea at USSR Institute for High igh Energy Physics in Energy Physics in ProtvinoProtvino. A 148.5. A 148.5--MHz RFQ accelerated 100MHz RFQ accelerated 100--KeV KeV protons to 620 protons to 620 KeVKeV with an efficiency of 50%.with an efficiency of 50%.1977 RFQ concept is published in the western world. Strong 1977 RFQ concept is published in the western world. Strong interest in Los Alamos National Laboratory (USA). Decision to teinterest in Los Alamos National Laboratory (USA). Decision to test st the RFQ principle for possible application in development of higthe RFQ principle for possible application in development of highh--current lowcurrent low--emittanceemittance beams. Developments of computer codes for beams. Developments of computer codes for rfqrfq design.design.1979 Start of P.O.P. (Proof1979 Start of P.O.P. (Proof--ofof--principle experiment) at Los principle experiment) at Los Alamos . 425 MHz RFQ accelerates a 100Alamos . 425 MHz RFQ accelerates a 100--keV proton beam to 640 keV proton beam to 640 keVkeV with an efficiency of 90%, as predicted by the codes. (14 Feb. with an efficiency of 90%, as predicted by the codes. (14 Feb. 1980 ) 1980 ) Nowadays hundreds of RFQ accelerator are operating in the worldNowadays hundreds of RFQ accelerator are operating in the world
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RFQ represented the RFQ represented the ““missing linkmissing link””to to high power beamhigh power beam
50%
90%
•High current and small emittance (powerful source)•High energy (powerful and efficient accelerators)
POWERFUL SOURCE :
200 mA proton beam
Emittance 1 pi mm mrad
POWERFUL
ACCELERATOR
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Link between source and efficient Link between source and efficient accelerator accelerator
The The RRadio adio FFrequency requency QQuadrupoleuadrupole is a linear is a linear accelerator which accelerator which
•• focusesfocuses•• bunchesbunches
•• accelerates accelerates a a continuoscontinuos beam of charged particles with high beam of charged particles with high
efficiency and preserving the efficiency and preserving the emittanceemittance
Both the focusing as well as the bunching and Both the focusing as well as the bunching and acceleration are performed by the RF fieldacceleration are performed by the RF field
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wave equation wave equation --recaprecap
Maxwell equation for E and B field:Maxwell equation for E and B field:
In In free spacefree space the electromagnetic fields are of the the electromagnetic fields are of the transverse electro transverse electro magnetic,magnetic,TEMTEM, type: the electric and magnetic field vectors are , type: the electric and magnetic field vectors are ⊥⊥ to each to each other and to the direction of propagation.other and to the direction of propagation.In a In a bounded mediumbounded medium (cavity) the solution of the equation must satisfy the (cavity) the solution of the equation must satisfy the boundary conditions : boundary conditions :
∂∂
∂∂
∂∂
∂∂
2
2
2
2
2
2 2
2
2
1 0x y z c t
E+ + −⎛⎝⎜
⎞⎠⎟ =r
0//
rr=E
0rr
=⊥B
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TE or TM modesTE or TM modes
TE (=transverse electric) : the electric field is TE (=transverse electric) : the electric field is perpendicular to the direction of propagation. perpendicular to the direction of propagation. in a cylindrical cavityin a cylindrical cavity
TM (=transverse magnetic) : the magnetic TM (=transverse magnetic) : the magnetic field is perpendicular to the direction of field is perpendicular to the direction of propagationpropagation
TEnml
nmlTM n : azimuthal,
m : radial
l longitudinal component
n : azimuthal,
m : radial
l longitudinal component
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TE modesTE modes
dipole mode quadrupole mode used in Radio Frequency Quadrupole
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Radio Frequency Radio Frequency QuadrupoleQuadrupole
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Radio Frequency Radio Frequency QuadrupoleQuadrupole
cavity loaded with 4 electrodes
TE210 mode
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RFQ StructuresRFQ Structures
fourfour--vanevane
fourfour--rodrod
others (split others (split coaxial,doublecoaxial,double H )H )
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four vanefour vane--structurestructure1. capacitance between
vanetips, inductance in the intervane space
2. each vane is a resonator
3. frequency depends on cylinder dimensions (good at freq. of the order of 200MHz, at lower frequency the diameter of the tank becomes too big)
4. vane tip are machined by a computer controlled milling machine.
5. need stabilization (problem of mixing with dipole modeTE110)
vane
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four rodfour rod--structurestructure
capacitance between rods, inductance with holding barscapacitance between rods, inductance with holding barseach cell is a resonatoreach cell is a resonatorcavity dimensions are independent from the frequency, cavity dimensions are independent from the frequency, easy to machine (lathe)easy to machine (lathe)problems with end cells, less efficient than 4problems with end cells, less efficient than 4--vane due to strong current in the vane due to strong current in the holding barsholding bars
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transverse field in an RFQtransverse field in an RFQalternating gradient focussing structure with period length βλ(in half RF period the particles have travelled a length βλ/2 )
+
-
-
+
+
- -
+
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transverse field in an RFQtransverse field in an RFQ
animation!!!!!
timeRF signal
....
t0 t1 t2 t3 t4
DT1 DT3 DT5
DT2 DT4
DT1,DT3...... t0,t1,t2........ DT2,DT4.....
+
+
- - + +
-
-
ion beam
electrodes
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acceleration in RFQacceleration in RFQ
longitudinal modulation on the electrodes creates a longitudinalcomponent in the TE mode
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acceleration in an RFQacceleration in an RFQ
longitudinal radius of curvature
beam axis
aperture
modulation X aperture
)2
1(2 π
ϕβλ Δ−
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important parameters of the RFQimportant parameters of the RFQ
( ) ( )( ) ( )⎟
⎟⎠
⎞⎜⎜⎝
⎛+
+⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
mkaIkaImmkaIkaI
afaV
mqB
oo
oo22
0
11
42
)()(1
2
2
0π
λβ ⋅⋅
+−
= VmkaIkaIm
mTEoo
Accelerating efficiency : fraction of the field deviated in the longitudinal direction(=0 for un-modulated electrodes)
transit time factor cell
length
Transverse field distortion due to modulation (=1 for un-modulated
electrodes)type of particle
limited by sparking
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.....and their relation .....and their relation
( ) ( )( ) ( )
1)()()(
102
2
2 =⋅+−
+⎟⎟⎠
⎞⎜⎜⎝
⎛
++ kaI
mkaIkaImm
mkaIkaImmkaIkaI
oooo
oo
a=bore radius, β,γ=relativistic parameters, c=speed of light, f= rf frequency, I0,1=zero,first order Bessel function, k=wave number, λ=wavelength, m=electrode modulation, m0=rest q=charge, r= average transverse beam dimension, r0=average bore, V=vane voltage
focusing efficiency
accelerating efficiency
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Beam dynamics design Beam dynamics design (very first approach)(very first approach)
The beam dynamics in an RFQ determined by the The beam dynamics in an RFQ determined by the geometrical parameter of the electrode structure geometrical parameter of the electrode structure
ApertureAperture : determines the focusing : determines the focusing strenghtstrenght and and the acceptance.the acceptance.
Depth of the modulationDepth of the modulation : determines the field : determines the field availibleavailible for acceleration for acceleration
Distance between the peaks and the troughDistance between the peaks and the trough of the of the modulation determines the synchronicity modulation determines the synchronicity between the field and the particles between the field and the particles
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Electrode structure Electrode structure
longitudinal radius of curvature
beam axis
aperture
modulation X aperture
)2
1(2 π
ϕβλ Δ−
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Transverse planeTransverse plane--focusing focusing • quadrupole focusing (1)
• RF defocusing ( modulation ) (2)• space charge defocusing (3)
( ) ( )σ
ππ ϕ λ
βγλ
π γ= − −
−B qE Tmc
Z qI f pmc r b
2
20
2 30
3
2 3 283 1
8sin ( )
Z0 is the free-space impedance (376.73 Ohm),I is the beam current, f(p) is a geometrical factorp is the ratio of the transvesebeam dimensions,r is the average transverse beam dimension, b the longitudinal .
(1) (2) (3)
0 90degσ <
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Longitudinal planeLongitudinal plane--bunchingbunching
timeRF signal
continous beam
bunched beam
Smootly change the velocity profile of the beam without changing its average energy
90degSϕ = −
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Longitudinal planeLongitudinal plane--accelerationacceleration
synchr. part.
early part.
late part. use the rising part of the RF : receive less acceleration,late particles more (PHASE FOCUSING)
90deg 0Sϕ− < <
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Radial matching to adapt the beam to a time-varying focusing system aperture smoothly
brought to the average value
shaping to give the beam a longitudinal structure Taper phase to –80,–60 deg
start modulation
aperture such that focusing is constant
bunching to bunch and begin acceleration Taper phase to –30,-20 deg
modulation to max
aperture such that focusing is constant
acceleration to bring the beam to the final energy. Constant phase Constant modulation Constant aperture output matching to adapt the beam to the downstream user’s need.
RFQ sections RFQ sections
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High intensity vs. low intensityHigh intensity vs. low intensity
Emittance dominated
Space charge dominated
RMS
over many cells w/o acceleration
SHAPER
shaping and acceleration
fast bunching PRE-BUNCHER
complete the bunching (almost no energy
increase up to here)
GENTLE BUNCHER
bunching and acceleration
fast transition to accelerating phase
BOOSTER
beam strongly bunched
(ϕ=-20,-15)
ACCELERATOR
beam bunched around ϕ=-35,-30
EXIT MATCHER
LOW INTENSITY RFQS CAN BE MADE SHORTER THAN THE CORRESPONDING HIGH INTENSITY ONES
LOW INTENSITY RFQS CAN BE MADE SHORTER THAN THE CORRESPONDING HIGH INTENSITY ONES
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HIGH INTENSITYHIGH INTENSITY RFQ2 ( 200 RFQ2 ( 200 mAmA protons)protons)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 20 40 60 80 100 120 140 160 180
z (cm)
mod
ulat
ion
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
phi (
deg)
synchronous phase
modulation
max value =-35
slow ramping from the beginning
modulation from the beginnig
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LOW INTENSITY LOW INTENSITY LEAD ION RFQ (100 LEAD ION RFQ (100 μμA )A )
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 20 40 60 80 100 120 140 160 180
z (cm)
mod
ulat
ion
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
phi (
deg)
modulation
synchronous phase
fast bunching
boosting
max value = -23
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Why is the RFQ such a good focusing Why is the RFQ such a good focusing channel for low energy ionschannel for low energy ions
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RFQ vs. DTLRFQ vs. DTL
DTL can't accept low velocity particles, there is a minimum injection energy in a DTL due to mechanical constraints
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Why is the RFQ so efficient in Why is the RFQ so efficient in bunching a beambunching a beam
Discrete bunching Discrete bunching
Vs adiabatic bunching : movie Vs adiabatic bunching : movie
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Why is the RFQ so efficient in Why is the RFQ so efficient in bunching a beambunching a beam
Discrete bunching Discrete bunching
Vs adiabatic bunching : movie Vs adiabatic bunching : movie
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Why donWhy don’’t we accelerate to the final t we accelerate to the final energy by using only energy by using only RFQsRFQs ??
Accelerating effciency
0
0.1
0.2
0.3
0.4
0.5
0 50 100 150 200
z (cm)CERN RFQ2
Max accelerating efficiency is limited by geometry
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RFQRFQ--summarysummaryThe resonating mode of the cavity is a focusing modeThe resonating mode of the cavity is a focusing modeAlternating the voltage on the electrodes produces an Alternating the voltage on the electrodes produces an alternating focusing channelalternating focusing channel
A longitudinal modulation of the electrodes produces a A longitudinal modulation of the electrodes produces a field in the direction of propagation of the beam which field in the direction of propagation of the beam which bunches and accelerates the beam bunches and accelerates the beam
Both the focusing as well as the bunching and Both the focusing as well as the bunching and acceleration are performed by the RF fieldacceleration are performed by the RF field
The RFQ is the only linear accelerator that can accept The RFQ is the only linear accelerator that can accept a low energy CONTINOUS beam of particlesa low energy CONTINOUS beam of particles
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RFQRFQ--highlights highlights
electric focusing : accept low energy electric focusing : accept low energy beam beam adiabatic bunching : preserve beam adiabatic bunching : preserve beam quality, high capture (~90%) vs. 50% of quality, high capture (~90%) vs. 50% of discrete bunchingdiscrete bunching““one buttonone button”” machine, easy to operate machine, easy to operate (the transverse and longitudinal (the transverse and longitudinal dynamics are machined in the electrode dynamics are machined in the electrode microstructure)microstructure)
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Further readingFurther readingT.P.WANGLER, T.P.WANGLER, ””Space charge limits in linear Space charge limits in linear acceleratoraccelerator””,LA,LA--8388 (Los Alamos)8388 (Los Alamos)R.H.STOKES and T.P.WANGLER, R.H.STOKES and T.P.WANGLER, ””Radio Radio Frequency Frequency QuadrupoleQuadrupole and their and their applicationsapplications””,Annual,Annual Review of Nuclear and Review of Nuclear and Particle Science , 1989Particle Science , 1989K.R. CRANDALL,R.H.STOKES and K.R. CRANDALL,R.H.STOKES and T.P.WANGLER, T.P.WANGLER, ““ RF RF QuadrupoleQuadrupole Beam Beam dynamics Design studydynamics Design study””,1979 Linear Accelerator ,1979 Linear Accelerator ConferenceConferenceM.WEISS, M.WEISS, ““ Radio Frequency Radio Frequency QuadrupoleQuadrupole”” , , CERNCERN--PS/87PS/87--51 (CAS Aarhus,1986)51 (CAS Aarhus,1986)
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Some CodesSome Codes
PARMTEQMPARMTEQM--Los AlamosLos Alamos
TOUTATISTOUTATIS-- CEA CEA SaclaySaclay
LIDOSLIDOS--MRTI MoscowMRTI Moscow
DYNAMIONDYNAMION--ITEP MoscowITEP Moscow