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Kicker Magnet System
（Lumped magnet and Distributed magnet）
Lecturer : Izumi Sakai
Supervised by Eiji Nakamura (KEK)
e-mail : [email protected]
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 ).
1
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
2
[A.1] Field Requirements for Beam Handling
3
Flow Chart of Fast Injection
Bunched beams circulate
Synchrotron Ring
Orbit Switching Device
( Kicker )
Injected beam
Field Pattern Requirement for Kicker
4
5
[A.2] Classification by Field Structure
6
“Electric” or “Magnetic” ?
Kinetic

Equation
d p
F = dt = q ( E +   B)
・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 fastrise/fall time.
7

For v  c
F  eE  e 
V
a
F  ecB
V= E a ~ a c B ~ a c
V  acB
0 I
a
~ 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.
8
[A.3] Transmission Theory
Resistance load case
V f + Vr = V
I f － Ir = I
V f = Z 0 I f and Vr = Z 0 I r
2V f = V + Z 0 I
2Vr = V －Z 0 I
V =ZI
Inductance load case
9
[B.1] Lumped type and Distributed Delay Line type
10
Typical structure of ladder-type kicker magnet
11
Schematic drawing of the ladder-type kicker magnet
and it’s equivalent circuit
12
Fundamental equations for the kicker magnet
The response of a ladder-type network for the waves of angular
frequency ω is given by next equation. (For steady state)


Vn1  1   2 Lc Vn  jLI n




I n1  jc 2   Lc Vn  1   Lc I n
2
2
(1)
If the unit ladder-type networks are connected infinitely,
the wave equation of the circuit is given by,
Vn
I
 n  e  j
Vn 1 I n 1
Vn Vn 1

Z
I n I n 1
(θ is the phase delay of the unit ladder)
(2)
(Z is the impedance for angular frequency ω)
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By substituting Eq. (2) to Eq. (1), we can get,
Z
Z0
1


 sin
c
2
 c 
Here, Z 0 
2
L
2c
c 
2
Lc
(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 Z0  L 2c
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,


2

 2 Lc
 c
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The rise time of the Kicker magnet is given by
T  Td  Tr
Where the Tr is the rise time of the PFN.
Td is the propagation time in the kicker magnet.
Td  n 
nL
Z0
Where the “n” is the number of unit ladder in the kicker magnet
I peak
V0

2Z 0
15
[B.2] Simulation for multi-stage ladder circuit
Parameters of Model Kicker System for simulation
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
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(1) Most Simple Excitation
Vf , If (Z0)
V
I = u / Z0
L
Equivalent Circuit
Electric potential at the input
of a magnet
Forward Pulse
Excitation current
Integrated magnetic field
17
(2) L-R case
R = Z0
18
(3) Distributed cases
C ~ L / Z0^2
I
J1
J2
V1 = V
V2
L0/2
L0/2
Q1
C0/2
I
Q2
C0/2
J1
J2
V1 = V
V2
L0/3
Q1
C0/3
L0/3
Q2
C0/3
J3
V3
L0/3
Q3
C0/3
19
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,
20
but is different for a fast step pulse
Propagation of current through ten-stage ladder
J1
J2
J3
J4
J5
J6
J7
J8
J9
J10 ( last )
21
22
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.
23
[B.3] Delay Line Structure
J1
J2
J3
J4
J5
J6
J7
J8
J9
J10 ( last )
Beam
B
I
I
Capacitance of air gap between parallel plates is used. It is possible
to apply ceramic capacitors, instead of air gaps.
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Beam
B
I
I
I
Beam
B
I
...
...
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.
26
[C.1] Fundamental Elements
Typical Requirements:
Output Voltage 10 kV ~ 50 kV
Output Current 1 kA ~ 10 kA
Repetition Rate 1 pps ~ 1 kpps
Averaged Power
~ 10 kW
* “pps” means “pulses per second”.
* It is small in comparison with other magnets for accelerators.
Charger
Pulse Forming
Device
Switch
Coaxial Cables
27
[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.
Main Output Trigger
<a>
Time
s econd order
Charging Switch (single pulse)
Main Output Trigger
<b>
C >> C1
Time
C1
milli-second order
Charging Trigger
Inverter, Charging Switch (high repetition)
Charging Trigger
Main Output Trigger
<c>
Time
milli-second order
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[C.3] Pulse Forming
<Examples>
(i) Simple capacitor case
(ii) Pulse Forming Line (PFL)
Z
Z
Time
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.
This curve is adjusted with a time constant Lm Z.
Lm is an inductance of a lumped magnet.
L
Z
Time
30
[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.
31
Representative Operation Region of Semi-conductor Devices
32
[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.
33
[D.2] Beam Coupling Impedance, Cooling system for Heat-up
by Beam Induced Field
A magnet plays a role of a transformer,
transmits a part of an electric power
from a primary current which is a beam to a secondary,
and then reduses a beam power.
Power Supply
Circulating Beam,
which is same as a primary current.
Excitation Coil
and its feeder
Kicker Magnet
Heat-up problem is raised in case of high beam current.
Cooling systems are required for vacuum ducts, metal materials, … .
34
[E] Trials Now !
Various trials are being carried out. Some of those are shown here.
35
[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.
36
[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, … .
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References
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CERN/MPS/SR71-5.
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Instr. and Meth. A 607 (2009) 489.
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38
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published).
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