Upload
trinhphuc
View
219
Download
0
Embed Size (px)
Citation preview
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
A.C. Magnet Systems
Neil Marks,
CI, ASTeC, U. of Liverpool,
The Cockcroft Institute,
Daresbury,
Warrington WA4 4AD,
U.K. Tel: (44) (0)1925 603191
Fax: (44) (0)1925 603192
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Philosophy
1. Present practical details of how a.c. lattice magnets differ
from d.c. magnets.
2. Present details of the typical qualities of steel used in lattice
magnets.
3. Give a qualitative overview of injection and extraction
techniques as used in circular machines.
4. Present the standard designs for kicker and septum magnets
and their associated power supplies.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Contents
a) Variations in design and construction for a.c. magnets;
Effects of eddy currents;
‘Low frequency’ a.c. magnets
Coil transposition; eddy loss; hysteresis loss;
Properties and choice of steel;
Inductance in an a.c. magnet;
b) Methods of injecting and extracting beam;
Single turn injection/extraction;
Multi-turn injection/extraction;
Magnet requirements;
c) ‘Fast’ magnets;
Kicker magnets-lumped and distributed power supplies;
Septum magnets-active and passive septa;
Some modern examples.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Differences to d.c. magnets
A.c magnets differ in two main respects to d.c. magnets:
1. In addition to d.c ohmic loss in the coils, there will be ‘ac’ losses
(eddy and hysteresis); design goals are to correctly calculate and
minimise a.c. losses.
2. Eddy currents will generate perturbing fields that will affect the beam.
3. Excitation voltage now includes an inductive (reactive) component;
this may be small, major or dominant (depending on frequency); this
must be accurately assessed.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Equivalent circuit of a.c. magnet
Lm Rdc
Cleakage
Im
Rac
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Additional Maxwell equation for magneto-dynamics:
curl E = -dB/dt.
Applying Stoke’s theorem around any closed path s enclosing area A:
curl E.dA = E.ds = V loop
where Vloop is voltage around path s;
- (dB /dt).dA = - dF/dt;
Where F is total flux cutting A;
So: Vloop = -dF/dt
Thus, eddy currents are induced in any conducting material in the alternating
field. This results in increased loss and modification to the field strength and
quality.
A.C. Magnet Design
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Eddy Currents in a Conductor I
Rectangular cross section resistivity ,
breadth 2 a ,
thickness ,
length l ,
cut normally by field B sin t.
Consider a strip at +x, width x , returning at –x ( l >>x).
Peak volts in circuit = 2 x l B
Resistance of circuit = 2 l /( x )
Peak current in circuit = x B x /
Integrate this to give total Amp-turns in block.
Peak instantaneous power in strip = 2 x2 l 2 B2 x /
Integrate w.r.t. x between 0 and a to obtain peak instantaneous power in block = (2/3) a3 l 2 B2 /
Cross section area A = 2 a
Average power is ½ of above.
Power loss/unit length = 2 B2 A a2/(6 ) W/m;
a 10x10 mm2 Cu conductor in a 1T 50Hz sin. field, loss = 1.7 kW/m
x
l
-a -x 0 x a
B sin t
Cross
section A
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Eddy Currents in a Conductor II
Circular cross section:
resistivity ,
radius a ,
length l ,
cut normally by field B sin t.
Consider a strip at +x, width x , returning at –x ( l >>x).
Peak volts in circuit = 2 x l B
Resistance of circuit = 2 l /{ 2 (a2-x2)1/2 x }
Peak current in circuit = 2x B (a2-x2) 1/2 x /
Integrate this to give total Amp-turns in block.
Peak instantaneous power in strip = 4 x2 l 2 B2 (a2-x2) 1/2 x /
Integrate w.r.t. x between 0 and a to obtain peak instantaneous power in block
= (p/4) a4 l 2 B2 /
Cross section area A = pa
Average power is ½ of above.
Power loss/unit length = 2 B2 A a2/(8 ) W/m;
x
a
x
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Eddy Currents in a cylindrical vacuum
vessel
R
q
q
B sin t
Geometry of cylindrical vacuum vessel,
:/2 0,between w.r.t.above
of integral iscylinder in current eddy total
;/ t) (cos B ) (cos R 2 I
:loops bottom and in top currentseddy
) R ( / 2
:loop oflength unit of resistance
t); cos )(B cos (R 2 V
:only) (top loop oflength unit round voltage
t); cos )(B cos (R 2 t /
);t sin B )( cos R ( 2
2e
pq
q
q
q
q
total flux cutting circuit at angle q:
Ie = - 2 R2 B (cos t) /
It can be seen that the eddy currents vary as the square of the cylindrical radius R and
directly with the wall thickness t.
Wall
conductivity
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Perturbation field generated by eddy
currents
Magnet geometry around vessel
radius R.
g
m =
R
x 0
Note:
•that if the vacuum vessel is between the poles of a
a ferro-magnetic yoke, the eddy currents will
couple to that yoke; the yoke geometry therefore
determines the perturbing fields;
•this analysis assumes that the perturbing field is
small compared to the imposed field.
Using: Be= m0 Ie/g;
Amplitude ratio between perturbing and imposed fields at X = 0 is:
Be(0)/B = - 2 m0 R2 / g;
Phase of perturbing field w.r.t. imposed field is:
qe = arctan (- 2 m0 R2 / g )
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Distributions of perturbing fields
Cylindrical vessel (radius R):
Be(X)
Rectangular vessel (semi axies a, b):
Be(X)
Elliptical vessel (semi axies a, b):
Be(X)
m
2/12222
1/2221/2221-
22
2 0
a 1) - b/ (a X b
) X - a ( )b a(tan
)b (a
b a
g
t cos B 2
m ab
2
)Xa(
g
t) cos (B 2
220
. X - R g
t Bcos oR2 22
m
m ............
R 128
X 5
R 16
X
R 8
X
R 2
X 1
g
t Bcos R o2
8
8
6
6
4
4
2
22
variation with horizontal position X
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Stainless steel vessels – amplitude.
Example: Ratio of amplitude of perturbing eddy current dipole field to amplitude of imposed
field as a function of frequency for three values of s.s. vessel wall thickness (R = g/2):
0.0001
0.001
0.01
0.1
1
1 10 100 1000
Frequency (Hz)
Pertu
rb
ati
on
/im
po
sed
fie
ld .
thickness= 0.25 mm thickness = 0.5 mm thickness = 1 mm
Calculation
invalid in this
region.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Stainless steel vessels – phase.
Phase change (lag) of dipole field applied to beam as a function of frequency for three
values of vessel wall thickness (R = g/2):
0.01
0.1
1
10
100
1 10 100 1000
Frequency (Hz)
Ph
ase
ch
an
ge i
n f
ield
ap
pli
ed
to
bea
m ;
(d
eg
rees)
thickness = 0.25 mm thickness = 0.5 mm thickness = 1 mm
Calculation
invalid in this
region.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
0
1.5
0 50 100 150 200
frequency (Hz)
‘Low frequency’ a.c. magnets
We shall deal separately with ‘low frequency’ and ‘fast’ magnets:
‘low frequency’
– d.c. to c 100 Hz:
‘fast’ magnets
– pulsed magnets with rise times from 10s ms to < < 1 ms.
(But these are very slow compared to r.f. systems!) time (ms)
0 ~10
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
c d
b a b a
d c
d c
b a
c d
a b
Coils for up to c 100 Hz.
Coil designed to avoid excessive eddy currents. Solutions:
a) Small cross section copper per turn; this give large number of turns - high
alternating voltage unless multiple conductors are connected in parallel; they
must then be ‘transposed’:
b) ‘Stranded’ conductor (standard solution in electrical engineering) with
strands separately insulated and transposed (but problems locating the
cooling tube!):
Flux density at the coil is predicted by f.e.a. codes, so eddy loss in coils can
be estimated during magnet design.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Two examples:
Note that eddy loss varies as 2 ; B2, (width)2 and cross-
section area.
NINA : E = 5.6 GeV;
= 53 Hz;
Bpeak = 0.9 T.
ISIS: E = 800 MeV;
= 50 Hz;
Bpeak ≈ 0.2 T.
Transposed, stranded conductor.
Cooling tube.
}c 10mm x 10 mm solid
conductor with cooling hole.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Steel Yoke Eddy Losses.
At 10 Hz lamination thickness of 0.5mm to 1
mm can be used.
At 50Hz, lamination thickness of 0.35mm to
0.65mm are standard.
Laminations also allow steel to be ‘shuffled’
during magnet assembly, so each magnet
contains a fraction of the total steel production;
- used also for d.c. magnets.
To limit eddy losses, steel core are laminated, with a thin layer
(~2 µm) of insulating material coated to one side of each
lamination.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Steel hysteresis loss
Steel also has hysteresis loss caused by the finite area inside the
B/H loop:
Loss is proportional to B.dH
integrated over the area
within the loop.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Steel loss data
Manufacturers give figures for total loss (in W/kg) in their steels catalogues:
•for a sin waveform at a fixed peak field (Euro standard is at 1.5 T);
•and at fixed frequency (50 Hz in Europe, 60 Hz in USA);
•at different lamination thicknesses (0.35, 0.5, 0.65 & 1.0 mm typically)
• they do not give separate values for eddy and hysteresis loss.
Accelerator magnets will have:
•different waveforms (unidirectional!);
•different d.c. bias values;
•different frequencies (0.2 Hz up to 50 Hz).
How does the designer calculate steel loss?
0
3
0 10
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Comparison between eddy and
hysteresis loss in steel:
Variation with: Eddy loss Hysteresis loss
A.c. frequency: Square law Linear;
A.c. amplitude: Square law Non-linear-depends on level;
D.c. bias: No effect Increases non-linearly;
Total volume of steel: Linear Linear;
Lamination thickness: Square law No effect.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Choice of steel
'Electrical steel' is either 'grain oriented' or 'non-oriented‘:
Grain oriented:
• strongly anisotropic,
• very high quality magnetic properties and very low a.c losses
in the rolling direction;
• normal to rolling direction is much worse than non-oriented
steel;
• stamping and machining causes loss of quality and the
stamped laminations must be annealed before final assembly.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Choice of steel (cont).
Non-oriented steel:
• some anisotropy (~5%);
• manufactured in many different grades, with different
magnetic and loss figures;
• losses controlled by the percentage of silicon included in the
mix;
• high silicon gives low losses (low coercivity), higher
permeability at low flux density but poorer magnetic
performance at high field;
• low (but not zero) silicon gives good performance at high B;
• silicon mechanically ‘stabilises’ the steel, prevents aging.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Solid steel
Low carbon/high purity steels:
• usually used for solid d.c. magnets;
• good magnetic properties at high fields
• but hysteresis loss not as low as high silicon steel;
• accelerator magnets are seldom made from solid steel;
(laminations preferred to allow shuffling and reduce eddy
currents)
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Comparisons
Property: DK-70: CK-27: 27 M 3: XC06 :
Type Non- Non- Grain- Non-
oriented oriented oriented oriented
Silicon content Low High - Very low
Lam thickness 0.65 mm 0.35 mm 0.27 mm Solid
a.c. loss (50 Hz):
at 1.5 T peak 6.9 W/kg 2.25 W/kg 0.79 W/kg Not suitable
Permeability:
at B=1.5 T 1,680 990 > 10,000 >1,000
at B=1.8 T 184 122 3,100 >160
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
The ‘problem’ with grain oriented steel
In spite of the
obvious advantage,
grain oriented is
seldom used in
accelerator magnets
because of the mechanical
problem of keeping B
in the direction of the grain.
B
Rolli ng
direction .
Difficult (impossible?) to make
each limb out of separate strips
of steel.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Magnet Inductance
Definition:
Inductance: L = n F /I
Dipole Inductance.
For an iron cored dipole:
F = B A = µ0 n I A/(g +l/µ);
Where: A is total area of flux (including gap fringe flux);
l is path length in steel;
g is total gap height
So: Lm = µ0 n2 A/(g +l/µ);
Note that the f.e.a. codes give values of vector potential to
provide total flux/unit length.
F
n turns,
current I
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Inductances in series and parallel.
Two coils, inductance L, with no mutual coupling:
Inductance in series = 2 L:
Inductance in parallel = L/2:
ie, just like
resistors.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
But
Two coils, inductance L, on the same core (fully
mutually coupled):
Inductance of coils in series = 4 L
n is doubled, n2 is quadrupled.
Inductance of coils in parallel = L
same number of turns, cross
section of conductor is doubled.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
The Injection/Extraction problem.
Single turn injection/extraction:
a magnetic element inflects beam into the ring and turn-off before the beam
completes the first turn (extraction is the reverse).
Multi-turn injection/extraction:
the system must inflect the beam into
the ring with an existing beam circulating
without producing excessive disturbance
or loss to the circulating beam.
Accumulation in a storage ring:
A special case of multi-turn injection - continues over many turns
(with the aim of minimal disturbance to the stored beam).
straight section
injected
beam
magnetic
element
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Single turn – simple solution
A ‘kicker magnet’ with fast turn-off (injection) or turn-on
(extraction) can be used for single turn injection.
injection – fast fall extraction – fast rise
Problems:
i) rise or fall will always be non-zero loss of beam;
ii) single turn inject does not allow the accumulation of high current;
iii) in small accelerators revolution times can be << 1 ms.
iv) magnets are inductive fast rise (fall) means (very) high voltage.
B
t
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Multi-turn injection solutions
Beam can be injected by phase-space manipulation:
a) Inject into an unoccupied outer region of phase space with non-integer tune
which ensures many turns before the injected beam re-occupies the same
region (electrons and protons):
eg – Horizontal phase space at Q = ¼ integer:
x
x’
turn 1 – first injection turn 2 turn 3 turn 4 – last injection
septum
0 field deflect. field
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Multi-turn injection solutions
b) Inject into outer region of phase space - damping coalesces beam into the
central region before re-injecting (high energy leptons only):
dynamic aperture
injected beam next injection after 1 damping time stored beam
c) inject negative ions through a bending magnet and then ‘strip’ to produce a p after
injection (H- to p only).
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Multi-turn extraction solution
‘Shave’ particles from edge of beam into an extraction channel
whilst the beam is moved across the aperture:
beam movement
extraction channel
Points:
•some beam loss on the septum cannot be prevented;
•efficiency can be improved by ‘blowing up’ on 1/3rd or 1/4th integer resonance.
septum
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Magnet requirements
Magnets required for injection and extraction systems.
i) Kicker magnets:
•pulsed waveform;
•rapid rise or fall times (usually << 1 ms);
•flat-top for uniform beam deflection.
ii) Septum magnets:
•pulsed or d.c. waveform;
•spatial separation into two regions;
•one region of high field (for injection deflection);
•one region of very low (ideally 0) field for existing beam;
•septum to be as thin as possible to limit beam loss.
Septum magnet
schematic
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Fast Magnet & Power Supplies
Because of the demanding performance required from these
systems, the magnet and power supply must be strongly
integrated and designed as a single unit.
Two alternative approaches to powering these magnets:
Distributed circuit: magnet and power supply made up of delay line circuits.
Lumped circuits: magnet is designed as a pure inductance; power supply can
be use delay line or a capacitor to feed the high pulse current.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
High Frequency – Kicker Magnets
Kicker Magnets:
•used for rapid deflection of beam for injection or extraction;
•usually located inside the vacuum chamber;
•rise/fall times << 1µs.
•yoke assembled from high frequency ferrite;
•single turn coil;
•pulse current 104A;
•pulse voltages of many kV.
beam
Conductors
Ferrite Core
Typical geometry:
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Kickers - Distributed System
Standard (CERN) delay line magnet and power supply:
dc
L, C L, C
Z 0
Power Supply Thyratron Magnet Resistor
The power supply and interconnecting cables are matched to the surge
impedance of the delay line magnet:
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Distributed System -mode of operation
•the first delay line is charged to by
the d.c. supply to a voltage : V;
•the thyratron triggers, a voltages wave: V/2 propagates into magnet;
•this gives a current wave of V/( 2 Z )
propagating into the magnet;
•the circuit is terminated by pure resistor Z,
to prevent reflection.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
EEV Thyratron CX1925
EEV
HV = 80kV
Peak current 15 kA
repetition 2 kHz
Life time ~3 year
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Magnet Physical assembly
Magnet:
Usually capacitance is introduced along the length of
the magnet, which is split into many segments:
ie it is a pseudo-
distributed line
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Power supplies for distributed systems.
Can be:
•a true ‘line’ (ie a long length of high voltage
coaxial cable);
•or a multi-segment lumped line.
These are referred to as ‘pulse forming networks’ (p.f.n.s) and are
used extensively in ‘modulators’ for:
• linacs;
• radar installations.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Parameters
The value of impedance Z (and therefore the added distributed
capacitance) is determined by the required rise time of current:
total magnet inductance = L;
capacitance added = C;
surge impedance Z0 = (L/C);
transit time (t) in magnet = (LC);
so Z0 = L/t;
for a current pulse (I), V = 2 Z I ;
= 2 I L / t .
The voltage (V/2) is the same as that required for a linear rise
across a pure inductance of the same value – the distributed
capacitance has not slowed the pulse down!
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Suitability of distributed system:
Strengths:
• the most widely used system for high I and V applications;
• highly suitable if power supply is remote from the magnet;
• this system is capable of very high quality pulses;
• other circuits can approach this in performance but not improve on it;
• the volts do not reverse across the thyratron at the end of the pulse.
Problems:
• the pulse voltage is only 1/2 of the line voltage;
• the volts are on the magnet throughout the pulse;
• the magnet is a complex piece of electrical & mechanical engineering;
• the terminating resistor must have a very low inductance - problem!
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Distributed power supply– lumped
magnet
Ldc
R = Z
Z0
0
I = (V/Z) (1 – exp (-Z t /L)
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Example of such a distributed kicker
system
SNS facility (Brookhaven)– extraction kickers:
• 14 kicker pulse power
supplies & magnets;
• operated at a 60 Hz
repetition rate;
• kicks beam in 250 nS;
• 750nS pulse flat top.
kicker magnet inductance 0.76 -0.8 uH
magnet current 2 - 2.5 kA
blumlein PFN Voltage 35 kV
pulse current rise time 200nS
current pulse width 750 nS
pulse repetition 60 Hz
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Extraction systems layout
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Kicker p.f.n simulation model
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Simulated current waveform
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Kickers – Lumped Systems.
•The magnet is (mainly) inductive - no added distributed
capacitance;
•the magnet must be very close to the supply (minimises
inductance).
Ldc
R
I = (V/R) (1 – exp (- R t /L)
i.e. the same waveform as distributed power supply, lumped magnet systems..
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Improvement on above
Ldc
R
C
The extra capacitor C improves the pulse substantially.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Resulting Waveform
Example calculated for the following parameters:
Pulse Waveform
0
0.2
0.4
0.6
0.8
1
1.2
0.00E+00 2.00E-07 4.00E-07 6.00E-07
Time ms
mag inductance L = 1 mH;
rise time t = 0.2 ms;
resistor R = 10 W;
trim capacitor C = 4,000 pF.
The impedance in the lumped
circuit is twice that needed in the
distributed! The voltage to
produce a given peak current is the
same in both cases.
Performance: at t = 0.1 ms, current amplitude = 0.777 of peak;
at t = 0.2 ms, current amplitude = 1.01 of peak.
The maximum ‘overswing’ is 2.5%.
This system is much simpler and cheaper than the distributed system.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
An EMMA kicker magnet – ferrite cored
lumped system.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
EMMA Injection Kicker Magnet
Waveform
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Septum Magnets – ‘classic’ design.
Often (not always) located inside the vacuum and used to deflect
part of the beam for injection or extraction:
Yoke.
Single turn coil
Beam
The thin 'septum' coil on the front
face gives:
•high field within the gap,
•low field externally;
Problems: •The thickness of the septum must be
minimised to limit beam loss;
•the front septum has very high
current density and major heating
problems
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Multiple septa
These engineering problems can be partially overcome by using
multiple septa magnets (the septa can get thicker as the beams
diverge).
eg – KEK (3 GeV beam):
Operation: DC
Beam: H+
Energy: 3.0 GeV
Field strength: 0.41067 T (SEPEX-1)
0.75023 T (SEPEX-2)
0.87418 T (SEPEX-3)
1.00530 T (SEPEX-4)
Effective length: 0.9 m
Field flatness: +/- 0.1 %
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
‘Opposite bend’ septa magnets
KEK also use ‘opposite bend’ septum magnets at 50
GeV:
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Septum Magnet – eddy current design.
•uses a pulsed current through a
backleg coil (usually a poor design
feature) to generate the field;
•the front eddy current shield must be,
at the septum, a number of skin depths
thick; elsewhere at least ten skin
depths;
•high eddy currents are induced in the
front screen; but this is at earth
potential and bonded to the base plate
– heat is conducted out to the base
plate;
•field outside the septum are usually ~
1% of field in the gap.
- +
Single or multi turncoil
Eddy currentshield
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Comparison of the two types.
Classical: Eddy current:
Excitation d.c or low frequency pulse; pulse at > 10 kHz;
Coil single turn including single or multi-turn on
front septum; backleg, room for
large cross section;
Cooling complex-water spirals heat generated in
in thermal contact with shield is conducted to
septum; base plate;
Yoke conventional steel high frequency
material (ferrite or
thin steel lams).
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Example
Skin depth in material: resistivity ;
permeability m;
at frequency
is given by: d = (2 /µµ0 )
Example: EMMA injection and extraction eddy current septa:
Screen thickness (at beam height): 1 mm;
" " (elsewhere) – up to 10 mm;
Excitation 25 µs,
half sinewave;
Skin depth in copper at 20 kHz 0.45 mm
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Location of EMMA septum magnets
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
Design of the EMMA septum magnet
Inner steel yoke
is assembled
from 0.1mm
thick silicon
steel
laminations,
insulated with
0.2 mm coatings
on each side.
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
‘Out of Vacuum’ designs.
Benefits in locating the magnet outside the vacuum.
But a (metallic) vessel has to be inserted inside the magnet -the
use of an eddy current design (probably) impossible.
eg the upgrade to the APS septum (2002):
‘The designs of the six septum magnets required for the APS facility have
evolved since operation began in 1996. Improvements .. have provided
better injection/extraction performance and extended the machine
reliability...’
‘Currently a new synchrotron extraction direct-drive septum with the
core out of vacuum is being built to replace the existing, in-vacuum eddy-
current-shielded magnet.’
Neil Marks; ASTeC, U. of Liverpool, CI. AC Mags; Lecture to Cockcroft Institute, November/December 2009
‘New’ APS septum magnet.
Synchrotron extraction septum conductor assembly partially installed in the laminated
core.