Kicker Magnet System（ Lumped magnet and Distributed magnet ）

Lecturer : Izumi SakaiSupervised by Eiji Nakamura (KEK)

e-mail : eiji.nakamura@kek.jp

A distributed magnet used as Fast eXtraction of proton beams from KEK 12GeV-PS for K2K Long-baseline Neutrino Oscillation Experiment. 8 bunches circulate a synchrotron ring in h = 9 (an upper signal Ch.3), and are ejected (which are measured with using a CT at a downstream of extraction septa, a lower signal Ch.D) by seven kicker magnets (a middle signal Ch.C ).

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Contents(A) Introduction [1] Field Requirements for Beam Handling [2] Classification by Field Structure [3] Transmission Theory

(B) Magnet [1] Lumped type and Distributed Delay Line type [2] Simulation for multi-stage ladder circuit [3] Delay Line Structure

(C) Power Supply [1] Fundamental Elements [2] Charger [3] Pulse Forming [4] Switching Devices for High Voltage and Large Current Pulse

(D) Total System and Surroundings [1] Outgas and Vacuum System [2] Beam Coupling Impedance, Cooling system for Heat-up by Beam Induced Field

(E) Trials Now(F) Key terms to develop in future(*) References and Appendices

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[A.1] Field Requirements for Beam Handling

Ion Source

Linear Accelerator (LINAC)

Circular Accelerator (Synchrotron)

299,792,458 m/s

~ 3.3 ns/m

Injection Point(A)

(B)

(C)

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Synchrotron Ring

Bunched beams circulate

Injected beam

Orbit Switching Device ( Kicker )

Field Pattern Requirement for Kicker

Flow Chart of Fast Injection

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Close to circulating orbit and angleby Septum magnets

Last Orbit-Correction by kicker

Field effects onto each beam. Injected beam Circulating beamBumpSeptumKicker

Typical layout of beam injection/ejction

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[A.2] Classification by Field Structure

Kicker

for Injection / Fast Extraction / Ejection

Electric Kicker Magnetic Kicker

Electrode for Low Energy Accelerator

Space Charge Effect of Another Particlefor High Energy Accelerator

RF Kicker

Bunch Shaping

Injection / Extraction by Momentum Deviation

Bending Kicker Multi-pole Kicker

Lumped Magnet Distributed Magnet

Lumpedwith Head Cells

Perfect Line Kicker

(R&D)

High Field Kickerby using Non-linear Effect

...

Q-mag. and Sext.-mag. are used for Electron Storage Ring.Non-linear field is now under planning.

Most popular kicker.

Classification by Field Structure

E B

Head Cell :C, R, L, Diode, ...

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“Electric” or “Magnetic” ?  

・ Electric kicker Fast response, Simple structure, cheap Field is weak, due to the limitation of break down Magnetic kicker Field is enough, but it is difficult to achieve fast-rise/fall time.

Kinetic Equation

F = d pd t = q ( E + B )

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Magnetic Material

Magnetic Field

Magnet

Lorentz Force

Electric Field

Electrode

a

a

V = E a ~ a c B ~ a c0 Ia ~ c 0 I = 377 [ ] I

It is easier to produce 3 kA-pulse than 1 MV-pulse.Magnetic kicker is used for high-energy accelerator.Electric kicker is used for low-energy accelerator.

a

VeeEF ecBF

cv

acBV

For

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[A.3] Transmission Theory

Resistance load case

Inductance load case

IZVIZVV

IZVV

IZVIZV

III

VVV

r

f

rrff

rf

rf

==2

+=2

=and=

=

=+

0

0

00

－

－

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[B.1] Lumped type and Distributed Delay Line type

Charger

Condensor C

Switch

Lumped magnet Inductance L

Magnetic Field for Beam Handling

resonance curve depends on sqrt[CL]

Output forward pulse from pulse generator

Magnetic Field Waveform

Deterioration of current rise due to a time constant ( C Z0)

Deterioration of current rise due to a time constant (L/ Z0)

Improvement on current rise

Time delay due to L/Z0

Deterioration of current rise due to a time constant (L/ Z0)

Improvement on current rise/fall

Radiation damage on power supply is a serious problem. --> It is necessary to keep it far from a magnet, and to feed HV-transmission lines.

Transmission Line

Improvement by using Pulse Forming Line

Improvement by using a distributed type of a magnet

Distributed Magnet

Matched Resistor R = Z0

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Typical structure of ladder-type kicker magnet

11

Schematic drawing of the ladder-type kicker magnet and it’s equivalent circuit

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Fundamental equations for the kicker magnet

nnn

nnn

ILcVLccjI

LIjVLcV22

1

21

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1

The response of a ladder-type network for the waves of angular frequency ω is given by next equation. (For steady state)

If the unit ladder-type networks are connected infinitely, the wave equation of the circuit is given by,

ZI

V

I

V

eI

I

V

V

n

n

n

n

j

n

n

n

n

1

1

11

(θ is the phase delay of the unit ladder)

(Z is the impedance for angular frequency ω)

(1)

(2)

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By substituting Eq. (2) to Eq. (1), we can get,

c

ZZ 2

0

1

c

LZ

20 Lcc

2

2sin

c

Here,

(3)

(4)

In the case of 0< ω/ωc<0.5, Then 1< Z/Z0<1.15, ω/ωc~θ/2

For the angular frequency ω is less than 0.5ωc , Impedance is constant and phase delay θ is proportional to ω.

The series connection of the ladder circuits is considered to be a transmission line with its characteristic impedance of cLZ 20

Hence the phase delay θ is given as θ=ωτ, and from ω/ωc~θ/2,the phase delay per unit section is given as,

Lcc

22

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The rise time of the Kicker magnet is given by

rd TTT

0Z

nLnTd

0

0

2Z

VI peak

Where the Tr is the rise time of the PFN.Td is the propagation time in the kicker magnet.

Where the “n” is the number of unit ladder in the kicker magnet

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[B.2] Simulation for multi-stage ladder circuit

Magnet

Gap height 50 mm

Gap width 100 mm

Gap length 400 mm

Total inductance ~ 1 µH

Power Supply

Characteristic Impedance 10 ohm

Forward pulse flattop voltage 25 kV

Forward pulse flattop current 2.5 kA

Forward pulse current rise 100 kA/µs

Forward pulse rise time 40 ns

Total System

B-MAX. 0.63 (1.3) kG

Time constant of magnet 100 ns

Required total capacitance for a distributed magnet 0.01 µF

Transmission time through a distributed magnet 100 ns

Parameters of Model Kicker System for simulation

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(1) Most Simple Excitation

　　

Vf , If (Z0)I = u / Z0V

L

Equivalent Circuit Forward Pulse

Electric potential at the input of a magnet

Excitation current Integrated magnetic field

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(2) L-R case

R = Z0

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(3) Distributed cases

C ~ L / Z0^2

Q1 Q2

I J1 J2

V1 = V V2

L0/2 L0/2

C0/2 C0/2

Q2

J2

V2

L0/3

Q1

I J1

V1 = V

L0/3

C0/3 C0/3Q3

J3

V3

L0/3

C0/3

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Four stage CL ladder

Ten stage CL ladder

(C/2)- (CL)-…-(CL)-(C/2)//R)

* The last case is for (C/2) – (L) – (C/2) ladder. It is almost same as CL ladder for a low frequency, but is different for a fast step pulse 20

Propagation of current through ten-stage ladder

J2J1 J3 J5J4 J6 J8J7 J9 J10 ( last )

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Practical Limit of Distribution

Field quality improves for a large stage number, but it is finite for the following reasons in a practical case. 

1. Electric discharge and insulation Strong electric field induces break down over 100 kV/cm, roughly, so unit length and each curvature of edge of materials should be larger than 2.5 mm. Ceramic coating or other technique is used for such a protection. 

2. Deterioration of Integrated Flux It is necessary to share space for non-magnetic material to form a capacitance.   ※ It is usual to decide unit length about 2 ~ 3 cm.

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[B.3] Delay Line Structure

J2J1 J3 J5J4 J6 J8J7 J9 J10 ( last )

I

I

B

Beam

Capacitance of air gap between parallel plates is used. It is possible to apply ceramic capacitors, instead of air gaps.

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Magnet I

I

B

Beam

I

I

Magnet

I

I

B

Beam

......

A distance of each cell is limited by the electric insulation, 10 ~ 100kV/cm. 25

Corner treatment and Ceramic Coating on metal plates are used for suppression of breakdown due to an electric field concentration.

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[C.1] Fundamental Elements

Typical Requirements:

Output Voltage 10 kV ~ 50 kV Output Current 1 kA ~ 10 kA Repetition Rate 1 pps ~ 1 kpps * “pps” means “pulses per second”.

Averaged Power ~ 10 kW * It is small in comparison with other magnets for accelerators.

Charger Pulse Forming Device

SwitchCoaxial Cables

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[C.2] Charger

<a> DC charging: it is stable and cheap, but is limited to use for a low repetition with a large power loss. <b> Resonant charging: an electric efficiency is good, but a step-up transformer is required.<c> Command charging; inverter, … : an electric efficiency and feasibility are good.

Time

second order

Main Output Trigger

C >> C1

C1

Charging Switch (single pulse)

Time

milli-second order

Main Output Trigger

Charging Trigger

Inverter, Charging Switch (high repetition)

Time

milli-second order

Main Output TriggerCharging Trigger

<a>

<b>

<c>

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[C.3] Pulse Forming <Examples>

(i) Simple capacitor case

TimeC

Z

It reduces with a time constant CZ.

e– tC Z 0

(ii) Pulse Forming Line (PFL)

Z

Time

Z

High Voltage coaxial cables and Coaxial tubes, which are filled with dielectric materials; pure water, BaTiO3, etc., are popular as PFL

(iii) Pulse Forming Network (PFN)

Z

Time

Ringing appears.29

(iv) Non-step pulse and etc.

Z

Time

LThis curve is adjusted with a time constant Lm Z.Lm is an inductance of a lumped magnet.

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[C.4] Switching Devices for High Voltage and Large Current Pulse

“Thyratron” is most popular for kicker magnet system, because simple one-device system can produce high voltage large current pulses at fast response.

Trials using semi-conductor elements have been carried out.

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Representative Operation Region of Semi-conductor Devices

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[D.1] Outgas and Vacuum system

If a high field with fast rise is required, a kicker magnet should be installed in vacuum. Ferrite materials are porous with impurities, put them out for a long time, and then deteriorate vacuum quality.

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[D.2] Beam Coupling Impedance, Cooling system for Heat-up by Beam Induced Field

Circulating Beam,which is same as a primary current.

Kicker Magnet

Excitation Coiland its feeder

A magnet plays a role of a transformer,transmits a part of an electric powerfrom a primary current which is a beam to a secondary,and then reduses a beam power.

Power Supply

Heat-up problem is raised in case of high beam current. Cooling systems are required for vacuum ducts, metal materials, … .

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[E] Trials Now ! Various trials are being carried out. Some of those are shown here.

High Field Fast Rise

CompactLow costStable

LHC abort kicker 60 kA excitation (working now)

ATF kicker 3 ns rise

Semiconductor Switches Voltage Adder 50 kV, 1 kA, 10 ns

Fast-rise high-field with using non-linearcharacteristic of materials, now under developing at KEK.

ex) "Hyper Kicker", "Saturation Kicker"," Multi-turn Saturation Kicker" ... by E. Nakamura.High performance may be obtained by using B-Hcharacteristic as a clip-out effect.

Compact Magnet with usingthe other characteristics of materials.

Capacitance is formed by using dielectric characteristic of ferritematerials, r ~ 15. Figure shows the example of Coaxial layout.

HV

Air gap,where beams pass

(Return)

Breakdown at the material boundary is a serious problem.Some enegineering techniques are necessary for micro-structure treatment.

B

C

Ferrite

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[F] Key terms to develop in future

“How Fast and How Large Field” can you achieve ?!   ~ Examples to develop ~ [a] Power Supply ~ Pulse Power Engineering Techniques ~ (a.1) Charger: high power, high efficiency, … .(a.2) Pulse Forming Devices. Pulse Forming Network. Pulse Forming Line/Tube with using dielectric materials. PE, BaTiO3, pure water, … . Improvement with using Impulse excitation.(a.3) Switches New method for Vacuum tube or Gas-filled tube. Semiconductor.

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[b] Magnet (b.1) Optimization of magnet structure.(b.2) Finite distributed magnet for perfect matching of impedance.(b.3) Non-magnetic material magnet.(b.4) Q-, Sext.-, and non-linear magnets for beam injection at electron storage rings.(b.5) High field magnet with using a non-linear characteristic of materials.(b.6) Low beam coupling magnet and its measurement method.(b.7) Investigation and Modeling of Transient Characteristics of materials at fast response and high field.(b.8) BL measurement method: there is no reliable and accurate method to measure higher performance than conventional kickers now.  [c] Total Systems and the others (c.1) Vacuum system and Suppression of outgas, unfavorable discharge: double layer vacuum field, insulation techniques.(c.2) Low Level Control system, which enables various outputs of kicker fields.(c.3) New Injection/Ejection Scheme.(c.4) Modeling and Simulation of Fast response near a light velocity.

Time dominant 3-D, Formulation, … . 37

References[1] D. Fiander: “Hardware for a Full Aperture Kicker System for the CPS,” US Part. Accel. Conf. Chicago, 1971. CERN/MPS/SR71-5.[2] Takata, Koji et al.: “Full Aperture Kicker Magnets for KEK Proton Synchrotron,” KEK-PrePrint KEK–76–21 (1976).[3] T. Oki: “The bridged-T network lumped kicker: A novel fast magnetic kicker system for a compact synchrotron,” Nucl. Instr. and Meth. A 607 (2009) 489.[4] < http://psdata.web.cern.ch/psdata/www/Kickers/psparam.htm >.[5] < http://ps-div.web.cern.ch/ps-div/LHC-PS/LHC-PS.html >.[6] D. Neuffer: “Injection and/or Extraction and a Ring Cooler,” Nucl. Instr. and Meth. A 503 (2003) 374-376.[7] B. I. Grishanov et al.: “Very fast kicker with high repetition rate for accelerator applications,” Nucl. Instr. and Meth. A 396 (1997) 28-34.[8] D. Anicic et al.: “A fast kicker magnet for the PSI 600 MeV proton beam to the PSI ultra-cold neutron source,” Nucl. Instr. and Meth. A 541 (2005) 598-609.[9] Efstratios Efstathiadis et al.: “A fast non-ferric kicker for the muon (g-2) experiment,” Nucl. Instr. and Meth. A 496 (2003) 8-25.[10] L. J. Lindgren et al.: “Fast Kicker Magnet System,” Nucl. Instr. and Meth. 214 (1983) 175-178.[11] Gerd Stange: “A new delay-line kicker with capacitive loading sandwiches,” Nucl. Instr. and Meth. A 300 (1991) 425-430.[12] M. Kikuchi et al.: “Beam-transport system of KEKB,” Nucl. Instr. and Meth. A 499 (2003) 8-23.[13] T. Mitsuhashi et al.: “A Design of the Injection Scheme and a Construction of Model Kicker Magnet for the High Brilliance Lattice of the Photon Factory,” Proceedings of 10 th Symp. On Accelerator Sci. Tech. (JAERI-Conf.95-021), 1995, p.94.[14] Y. Ishi et al.: “High field, high repetition rate kicker,” Nucl. Instr. and Meth. A 472 (2001) 639-642.[15] Tomohiro Ohkawa et al.: “Development of the kicker magnet for muses,” Nucl. Instr. and Meth. A 547 (2005) 287-293.[16] W. Jiang, et al.: “Compact Solid-State Switched Pulsed Power and Its Application,” Proceedings of the IEEE, Vol. 92, No. 7, July 2004, 1180-1196.[17] W. Zhang, et al.: “Pulsed Power Applications in High Intensity Proton,” Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee, USA (2005) 568-572.

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[18] E. Nakamura, et al.: “Injection/Extraction Beam Dump Kicker Magnet Systems for MR of J-PARC,” Proceedings of the 4th Annual Meeting of Particle Accelerator Society of Japan and the 32nd Linear Accelerator Meeting in Japan, Wako, Japan, August 1-3, (2007) 787-789.[19] E. Nakamura, et al.: “A Modification Plan of the KEK 500 MeV Booster to an all ion accelerators (an injector-free synchrotron),” Proceedings of 2007 Particle Accelerator Conference, Albuquerque, New Mexico, USA, June 21-29 (2007) 1492.[20] Tanuja S. Dixit et al.: “Induction acceleration scenario from an extremely low energy in the KEK all-ion accelerator,” Nucl. Instr. and Meth. A 602 (2009) 326-336.[21] V. D. Shiltsev: “Beam-beam kicker for superfast bunch handling,” Nucl. Instr. and Meth. A 374 (1996) 137-143.[22] H. Barkhausen: Phys. Z. 20 (1919) 401.[23] M. Konuma: “Magnetic Materials,” Kohgaku-Tosho Co., Ltd., 1996, ISBN4-7692-0355-1 C3055 (in Japanese).[24] G. Nassibian and F. Sachere: “Method for Measuring Transverse Coupling Impedances in Circular Accelerator,” Nuclear Instruments and Methods 159 (1979) 21-27.[25] H. Hahn and A. Ratti: “On the Low-Frequency Coupling Impedance of Transmission Line Kickers,” AD/RHIC/RD-111 of BNL, March, 1997.[26] H. Hahn: “Equivalent Circuit Analysis of the RHIC Injection Kickers,” AD/RHIC/RD-112 of BNL, April, 1997.[27] E. Nakamura, et al.: “Beam Injection/Extraction for All-ion Accelerator (AIA),” Proceedings of the 9 th Accelerator and Related Technology for Application, TIT, Tokyo, Japan, June 21-22, 2007, 21p6.[28] E. Nakamura, et al.: “PoP-experiments of the all-ion accelerator,” Proceedings of 2007 Fall Meeting of the Atomic Energy Society of Japan, Fukuoka, Japan, Sept. 27-29, (2007) 135 (in Japanese).[29] < http://www-accps.kek.jp/staff/BEAM-Group/Kicker-Group/index.html >.[30] E. Nakamura: “Fast-rise high-field kicker magnet operating in saturation,” Nucl. Instr. and Meth. A (to be published).

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