a.c. magnet systems · neil marks; astec, ci. ac magnets; cockcroft institute, spring term 2013....
TRANSCRIPT
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
A.C. Magnet Systems
Neil Marks,
ASTeC, Cockcroft Institute,
Daresbury,
Warrington WA4 4AD,
[email protected] Tel: (44) (0)1925 603191
Fax: (44) (0)1925 603192
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Contents
a) Variations in design and construction for a.c. magnets;
Effects of eddy current in vac vessels and coils;
Properties and choice of steel;
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Equivalent circuit of a.c. magnet
Lm Rdc
Cleakage
Im
Rac
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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;
x
l
-a -x 0 x a
B sin t
Cross
section A
a 10x10 mm2
Cu conductor in a 1T peak 50Hz sin. field, loss = 1.7 kW/m
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Perturbation field generated by eddy
currents.
Note, eddy currents in vacuum vessels:
In all cases, the first order field perturbation is (a -X2) ;
→ reduction in dipole field and
negative sextupole adding to
negative chromaticity.
cylindrical and elliptical vessels also have 10, 14.. pole.
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Stainless steel vessels – amplitude loss.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
AC effects in steel yokes
Steel yokes will have:
• eddy current power loss - with distortion of B;
• hysteresis losses.
So have to be ‘laminated’
like a mains transformer.
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, the laminations in the steel core are
coated with a thin layer (~2 µm) of insulating material, usually
just on one side of each lamination.
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Distributed System -mode of operation
•the first delay line is charged by
the d.c. supply to a voltage : V;
•the thyratron triggers, a voltages wave: V/2
which 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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Improvement on above
Ldc
R
C
The extra capacitor C improves the pulse substantially.
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
An EMMA kicker magnet – ferrite cored
lumped system.
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
EMMA Injection Kicker Magnet
Waveform
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
Location of EMMA septum magnets
Neil Marks; ASTeC, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
‘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, CI. AC Magnets; Cockcroft Institute, Spring Term 2013.
‘New’ APS septum magnet.
Synchrotron extraction septum conductor assembly partially installed in the laminated
core.