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. Philosophy. Present practical details of how a.c. lattice magnets differ from d.c. magnets.
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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
Rac
Rdc
Lm
Im
Cleakage
dx
B sin wt
t
l
-a -x 0 x a
Cross section A
dx
a
x
dq
R
q
B sin w t
t
total flux cutting circuit at angle q:
Wall conductivity r
Ie = - 2 wt R2 B (cos wt) / r
Geometry of cylindrical vacuum vessel,
It can be seen that the eddy currents vary as the square of the cylindrical radius R and directly with the wall thickness t.
m =
g
R
0
x
Magnet geometry around vessel radius R.
Using: Be= m0 Ie/g;
Amplitude ratio between perturbing and imposed fields at X = 0 is:
Be(0)/B = - 2 m0 wt R2 / r g;
Phase of perturbing field w.r.t. imposed field is:
qe = arctan (- 2 m0 wt R2 / r g )
variation with horizontal position X
Calculation invalid in this region.
Calculation invalid in this region.
time (ms)
0
~10
d c
c d
a
b
b a
c d
a b
d c
b a
}c 10mm x 10 mm solid conductor with cooling hole.
To limit eddy losses, steel core are laminated, with a thin layer (~2 µm) of insulating material coated to one side of each lamination.
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.
Difficult (impossible?) to make each limb out of separate strips of steel.
F
n turns,
current I
Two coils, inductance L, with no mutual coupling:
Inductance in series = 2 L:
Inductance in parallel = L/2:
ie, just like resistors.
n is doubled, n2 is quadrupled.
Inductance of coils in parallel = L
same number of turns, cross section of conductor is doubled.
straight section
magnetic element
injected beam
B
t
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.
x’
x
septum
0 field deflect. field
turn 2
turn 3
turn 1 – first injection
turn 4 – last injection
dynamic aperture
stored beam
injected beam
next injection after 1 damping time
c) inject negative ions through a bending magnet and then ‘strip’ to produce a p after injection (H- to p only).
extraction channel
beam movement
septum
Septum magnet schematic
Typical geometry:
Power Supply Thyratron Magnet Resistor
The power supply and interconnecting cables are matched to the surge impedance of the delay line magnet:
EEV
HV = 80kV
Peak current 15 kA
repetition 2 kHz
Life time ~3 year
ie it is a pseudo-distributed line
I = (V/Z) (1 – exp (-Z t /L)
I = (V/R) (1 – exp (- R t /L)
i.e. the same waveform as distributed power supply, lumped magnet systems..
C
The extra capacitor C improves the pulse substantially.
mag inductance L = 1 mH;
rise timet = 0.2 ms;
resistorR = 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.
Inner steel yoke is assembled from 0.1mm thick silicon steel laminations, insulated with 0.2 mm coatings on each side.
Synchrotron extraction septum conductor assembly partially installed in the laminated core.