# Lecture 3: Cables and quenching

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```					                      Lecture 3: Cables and quenching

Cables
• why cables?
• coupling in cables
• effect on field error in magnets

Quenching
Rutherford cable
• the quench process, internal and
used in all superconducting                         external voltages
accelerators to date
• decay times and temperature rise
• propagation of the normal zone
• quench protection schemes
• protection of LHC

Martin Wilson Lecture 3 slide1   Superconducting Magnets for Accelerators JUAS Feb 2006
Why cables?
• for good tracking we connect synchrotron
magnets in series
• if the stored energy is E, rise time t and
operating current I , the charging voltage is
1                    L I 2E
E  LI 2           V       
2                     t    It
RHIC E = 40kJ/m, t = 75s, 30 strand cable
cable I = 5kA, charge voltage per km = 213V
wire I = 167A, charge voltage per km = 6400V

FAIR at GSI E = 74kJ/m, t = 4s, 30 strand cable
cable I = 6.8kA, charge voltage per km = 5.4kV
wire I = 227A, charge voltage per km = 163kV

• so we need high currents!
the RHIC tunnel
• a single 5mm filament of NbTi in 6T carries 50mA
• a composite wire of fine filaments typically has 5,000 to 10,000 filaments, so it carries 250A to 500A
• for 5 to 10kA, we need 20 to 40 wires in parallel - a cable

Martin Wilson Lecture 3 slide2          Superconducting Magnets for Accelerators JUAS Feb 2006
Types of cable
• cables carry a large current and this generates a                  I
self field                                                                               Bs
• in this cable the self field generates a flux between
the inner and outer wires 
• wire are twisted to avoid flux linkage between the
filaments, for the same reasons we should avoid
flux linkage between wires in a cable
• but twisting this cable doesn't help because the inner
wires are always inside and the outers outside

• thus it is necessary for the wires to be fully
transposed, ie every wire must change
places with every other wire along the
length of the cable so that, averaged
over the length, no flux is enclosed
• three types of fully transposed cable
have been tried in accelerators
- rope
- braid
- Rutherford

Martin Wilson Lecture 3 slide3            Superconducting Magnets for Accelerators JUAS Feb 2006
Rutherford
•                        cable

• the cable is insulated by wrapping 2 or 3 layers of Kapton; gaps may be left to allow penetration
of liquid helium; the outer layer is treated with an adhesive layer for bonding to adjacent turns.

outwards, don't bond it
to the cable (avoid
energy release by bond
failure, which could
quench the magnet )

Martin Wilson Lecture 3 slide4        Superconducting Magnets for Accelerators JUAS Feb 2006
Rutherford cable

•     The main reason why Rutherford
cable succeeded where others failed
was that it could be compacted to a
high density (88 - 94%) without
damaging the wires. Furthermore it
can be rolled to a good dimensional
accuracy (~ 10mm).
•     Note the 'keystone angle', which
enables the cables to be stacked
closely round a circular aperture

Martin Wilson Lecture 3 slide5          Superconducting Magnets for Accelerators JUAS Feb 2006
Coupling in Rutherford cables
•     Field transverse                                      
B             crossover resistance Rc
coupling via crossover resistance Rc                                adjacent resistance Ra

Ra   Rc

•    Field transverse                                • Field parallel
coupling via                                      coupling via
resistance Ra                                     resistance Ra

B


B

Martin Wilson Lecture 3 slide6           Superconducting Magnets for Accelerators JUAS Feb 2006
Magnetization from coupling in cables
B`

• Field transverse                            
1 Bt c
M tc           p N ( N  1)
coupling via crossover                  120 Rc b                                           2b
resistance Rc                                                                 2c
where M = magnetization per unit volume of cable, p twist pitch, N = number of strands

• Field transverse                                              
1 Bt c
coupling via adjacent resistance Ra                  M ta      p
6 Ra b
where q = slope angle of wires Cosq ~ 1

• Field parallel                                              
1 Bp b                 (usually
coupling via adjacent resistance Ra              M pa        p                  negligible)
8 Ra c

• Field transverse                             M tc Ra N ( N  1)     R
               45 a
ratio crossover/adjacent                     M ta Rc     20         Rc

So without increasing loss too much can make Ra 50 times less than Rc - anisotropy

Martin Wilson Lecture 3 slide7           Superconducting Magnets for Accelerators JUAS Feb 2006
Controlling Ra and Rc                                                  1000                                             bare copper
untreated Staybrite
nickel

• surface coatings on the wires are used                                                                                oxidized Stabrite

Resistance per crossover Rc m
100
• the values obtained are very sensitive
to pressure and heat treatments used in
coil manufacture (to cure the adhesive                                          10
between turns)
• data from David Richter CERN
1

0.1
0   50          100        150        200        250
Heat treatment temperature C
Cored Cables

• using a resistive core
allows us to increase Rc
preferentially
• not affected by heat
treatment

Martin Wilson Lecture 3 slide8        Superconducting Magnets for Accelerators JUAS Feb 2006
Long range coupling: BICCs
•     measuring the field of an accelerator
magnet along the beam direction, we
find a ripple
•     wavelength of this ripple exactly
matches the twist pitch of the cable
•     thought to be caused by non uniform
current sharing in the cable
•     Verweij has called them 'boundary
induced coupling currents' BICCs
•     they are caused by non uniform flux
linkages or resistances in the cable, eg
at joints, coil ends, manufacturing
errors etc.
•     wavelength is << betatron wavelength
so no direct problem, but interesting
secondary effects such as 'snap back'.                sextupole measured in SSC dipole at
injection and full field

Martin Wilson Lecture 3 slide9           Superconducting Magnets for Accelerators JUAS Feb 2006
Field errors caused by coupling
• plot of sextupole field                                     3
error in an LHC dipole                                                                   0 A/sec         20 A/s
with field ramped at                                        2                            35 A/s          50 A/s
different rates

sextupole field (Gauss)
• error at low field due to
1
filament magnetization
• error at high field due to
0
a) iron saturation
b) coupling between
strands of the cable                                        -1
• the curves turn 'inside
out' because                                                -2
- greatest filament
magnetization is in
-3
the low field region
(high Jc)                                                      0      1     2      3       4       5       6    7     8         9
- greatest coupling is in                                                                dipole field (T)
the high field region
(high dB/dt)                                                                                      data from Luca Bottura CERN

Martin Wilson Lecture 3 slide10                                      Superconducting Magnets for Accelerators JUAS Feb 2006
Cables: concluding remarks

• accelerator magnets need high currents  cables
- cables must be fully transposed
- Rutherford cable used in all accelerators to date

• can get coupling between strands in cables
- causes additional magnetization  field error
- control coupling by oxide layers on wires or resistive core foils

Martin Wilson Lecture 3 slide11          Superconducting Magnets for Accelerators JUAS Feb 2006
Part 2: Quenching
the most likely
cause of death
Plan                                                                         for a
superconducting
• the quench process                                                         magnet

• decay times and temperature rise

• propagation of the resistive zone

• resistance growth and decay times

• quench protection schemes

• case study: LHC protection

Martin Wilson Lecture 3 slide12          Superconducting Magnets for Accelerators JUAS Feb 2006
Magnetic stored energy
Magnetic energy density
B2
E                        at 5T E = 107 Joule.m-3         at 10T E = 4x107 Joule.m-3
2m o

LHC dipole magnet (twin apertures)

E = ½ LI 2 L = 0.12H I = 11.5kA
E = 7.8 x 106 Joules

the magnet weighs 26 tonnes
so the magnetic stored energy is
equivalent to the kinetic energy
of:-

26 tonnes travelling at 88km/hr

Martin Wilson Lecture 3 slide13                 Superconducting Magnets for Accelerators JUAS Feb 2006
The quench process
• resistive region starts somewhere
in the winding at a point
- this is the problem!

• it grows by thermal conduction

• stored energy ½LI2 of the magnet
is dissipated as heat

• greatest integrated heat
dissipation is at point where the
quench starts

• internal voltages much greater
than terminal voltage ( = Vcs
current supply)

• maximum temperature may be
calculated from the current decay
time via the U(q) function

Martin Wilson Lecture 3 slide14   Superconducting Magnets for Accelerators JUAS Feb 2006
The temperature rise function U(q)
or the 'fuse blowing' calculation

J 2 (T )  (q )dT   C (q )dq

J(T) = overall current density,
T = time,
(q) = overall resistivity,
 = density, q = temperature,
C(q) = specific heat,
TQ= quench decay time.

                        qm    C (q )

o
J 2 (T ) dT  
qo      (q )
dq

 U (q m )

J o TQ  U (q m )
2

• GSI 001 dipole winding is
50% copper, 22% NbTi,
16% Kapton and 3% stainless steel                        • NB always use overall current density

Martin Wilson Lecture 3 slide15         Superconducting Magnets for Accelerators JUAS Feb 2006
Measured current decay after a quench
8000                                                                 40

20
6000
0

coil voltage (V)
current (A)

4000                                                                 -20
current
V lower coil         -40
IR = L dI/dt
2000                                            V top coil
-60

0                                                                 -80
0.0     0.2              0.4            0.6             0.8
time (s)

Dipole GSI001 measured at Brookhaven National Laboratory

Martin Wilson Lecture 3 slide16          Superconducting Magnets for Accelerators JUAS Feb 2006
Calculating the temperature rise from the current
decay curve
 J 2 dt (measured)             U(q) (calculated)

6.E+16                                                                     6.E+16
integral (J2dt)

U(q) (A2sm-4)
4.E+16                                                                     4.E+16

2.E+16                                                                     2.E+16

0.E+00                                                                     0.E+00
0.0       0.2       0.4      0.60          200          400
time (s)                           temp (K)

Martin Wilson Lecture 3 slide17                  Superconducting Magnets for Accelerators JUAS Feb 2006
Calculated temperature

• calculate the U(q)
function from known
400                                                       materials properties
• measure the current
decay profile
300
temperature (K)

• calculate the maximum
temperature rise at the
point where quench
200                                                       starts
• we now know if the
temperature rise is
100                                                       acceptable
- but only after it has
happened!
0                                                     • need to calculate current
0.0       0.2              0.4              0.6     decay curve before
time (s)                            quenching

Martin Wilson Lecture 3 slide18              Superconducting Magnets for Accelerators JUAS Feb 2006
Growth of the resistive zone

the quench starts at a point and then grows
in three dimensions via the combined
effects of Joule heating and
thermal conduction

*

Martin Wilson Lecture 3 slide19           Superconducting Magnets for Accelerators JUAS Feb 2006
Quench propagation velocity 1
• resistive zone starts at a point and spreads
outwards                                                         resistive
• the force driving it forward is the heat generation                                      v
in the resistive zone, together with heat                    temperature     qt
conduction along the wire                                                              superconducting
• write the heat conduction equations with resistive
power generation J2 per unit volume in left                     qo
hand region and  = 0 in right hand region.                           distance    xt

     q       q
k A   C A     hP(q  q 0 ) + J 2  A  0
x    x       t

where: k = thermal conductivity, A = area occupied by a single turn,  = density, C = specific heat,
h = heat transfer coefficient, P = cooled perimeter,   resistivity, qo = base temperature
Note: all parameters are averaged over A the cross section occupied by one turn

assume xt moves to the right at velocity v and take a new coordinate e = x-xt= x-vt

d 2q v C dq h P              J 2
+          (q  q 0 ) +      0
de 2   k de k A                k

Martin Wilson Lecture 3 slide20               Superconducting Magnets for Accelerators JUAS Feb 2006
Quench propagation velocity 2
when h = 0, the solution for q which gives a continuous join between left and right sides at qt
1             1
J  k          J  Loqt 
2             2
recap Wiedemann Franz Law     (q).k(q) = Loq
vad                                
 C qt  q 0   C qt  q 0 

what to say about qt ?
• in a single superconductor it is just qc
• but in a practical filamentary composite wire the current transfers progressively to the copper
• current sharing temperature qs = qo + margin
• zero current in copper below qs all current in copper above qs
• take a mean transition temperature qs = (qs + qc ) / 2

Jc                                 Cu
Jop

eff

qo qs           qc          qo   qs   qt     qc

Martin Wilson Lecture 3 slide21              Superconducting Magnets for Accelerators JUAS Feb 2006
Quench propagation velocity 3
1
the resistive zone also propagates sideways through               vtrans  ktrans 
                    2
the inter-turn insulation (much more slowly)                                  
calculation is similar and the velocity ratio  is:               vlong  klong 
        

Typical values           vad = 5 - 20 ms-1     0.01  0.03
v            v
so the resistive zone advances in
v
the form of an ellipsoid, with its
long dimension along the wire

Some corrections for a better approximation
• because C varies so strongly with temperature, it is better                          H (q c )  H (q g )
Cav (q g ,q c ) 
to calculate an averaged C from the enthalpy change                                     (q c  q g )
• heat diffuses slowly into the insulation, so its heat capacity should be excluded from the
averaged heat capacity when calculating longitudinal velocity - but not transverse velocity
• if the winding is porous to liquid helium (usual in accelerator magnets) need to include a time
dependent heat transfer term
• can approximate all the above, but for a really good answer must solve (numerically) the three
dimensional heat diffusion equation or, even better, measure it!

Martin Wilson Lecture 3 slide22           Superconducting Magnets for Accelerators JUAS Feb 2006
Computation of resistance growth and current
decay
start resistive zone 1                                        vdt
vdt
*
in time dt zone 1 grows v.dt longitudinally and .v.dt transversely

temperature of zone grows by dq1  J2 (q1)dt /  C(q1)

resistivity of zone 1 is (q1)

calculate resistance and hence current decay dI = R / L.dt
vdt
vdt
in time dt add zone n:
v.dt longitudinal and .v.dt transverse

temperature of each zone grows by dq1  J2(q1)dt /C(q1) dq2  J2(q2)dt /C(q2) dqn  J2(q1)dt /C(qn)

resistivity of each zone is (q1) (q2) (qn) resistance r1= (q1) * fg1 (geom factor) r2= (q2) * fg2 rn= (qn) * fgn

calculate total resistance R =  r1+ r2 + rn.. and hence current decay dI = (I R /L)dt

when I  0 stop
Martin Wilson Lecture 3 slide23                   Superconducting Magnets for Accelerators JUAS Feb 2006
Quench starts in the pole region

*
*

the geometry factor fg depends on
where the quench starts in relation
to the coil boundaries

Martin Wilson Lecture 3 slide24          Superconducting Magnets for Accelerators JUAS Feb 2006
Quench starts in the mid plane

*

Martin Wilson Lecture 3 slide25     Superconducting Magnets for Accelerators JUAS Feb 2006
Computer simulation of quench (dipole
GSI001)
8000
pole block
2nd block
mid block
6000
current (A)

4000

2000
measured
pole block
2nd block
mid block
0
0.0            0.1      0.2           0.3                0.4   0.5          0.6
time (s)

Martin Wilson Lecture 3 slide26                Superconducting Magnets for Accelerators JUAS Feb 2006
Computer simulation of quench
temperature rise
600
pole block
2nd block
500                 mid block

400
temperature (K)

300

200

from measured
100                                                        pole block
2nd block
mid block
0
0.0            0.2                       0.4                         0.6
time (s)

Martin Wilson Lecture 3 slide27         Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
1) external dump resistor

• detect the quench electronically
• open an external circuit breaker
• force the current to decay with a time
constant

t
                           L
I  Ioe        t       where      t
Rp

• calculate qmax from

τ
2
Jo          U (q m )
2
Note: circuit breaker must be able to
open at full current against a voltage
V = I.Rp               (expensive)

Martin Wilson Lecture 3 slide28         Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
2) quench back heater

•    detect the quench electronically

•    power a heater in good thermal contact
with the winding

•    this quenches other regions of the
magnet, effectively forcing the normal
zone to grow more rapidly
 higher resistance
 shorter decay time
 lower temperature rise at the hot spot

Note: usually pulse the heater by a capacitor, the             method most commonly used
high voltages involved raise a conflict between:-               in accelerator magnets 
- good themal contact
- good electrical insulation

Martin Wilson Lecture 3 slide29        Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
3) quench detection (a)
I
dI
internal voltage    V  IRQ   L          + Vcs
after quench                        dt
V
• not much happens in the early stages -
t                          small dI / dt  small V
• but important to act soon if we are to
reduce TQ significantly
• so must detect small voltage
• superconducting magnets have large
inductance  large voltages during
charging
• detector must reject V = L dI / dt and pick
up V = IR
• detector must also withstand high voltage -
as must the insulation

Martin Wilson Lecture 3 slide30       Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
i) Mutual inductance
3) quench detection (b)
ii) Balanced potentiometer
• adjust for balance when not quenched
• unbalance of resistive zone seen as voltage
across detector D
D
• if you worry about symmetrical quenches
connect a second detector at a different point

detector subtracts voltages to give
di           di
V L           + IRQ  M                                                        D
dt           dt

• adjust detector to effectively make L = M
• M can be a toroid linking the current
supply bus, but must be linear - no iron!

Martin Wilson Lecture 3 slide31                Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
4) Subdivision
• resistor chain across magnet - cold in cryostat
I                    • current from rest of magnet can by-pass the resistive
section
• effective inductance of the quenched section is
reduced
 reduced decay time
 reduced temperature rise
• current in rest of magnet increased by mutual
inductance effects
 quench initiation in other regions
• often use cold diodes to avoid
shunting magnet when charging it
• diodes only conduct (forwards)
when voltage rises to quench levels
• connect diodes 'back to back' so
they can conduct (above threshold)
in either direction

Martin Wilson Lecture 3 slide32   Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
4b) Subdivision with quench back
heater

• arrange for the subdividing
resistors to be in thermal contact
with the winding

• each resistor to contact a remote
section of winding – spread the
quench around

Martin Wilson Lecture 3 slide33        Superconducting Magnets for Accelerators JUAS Feb 2006
Methods of quench protection:
5) coupled secondary

• arrange for the winding to be closely
coupled to a short circuited secondary

• typically the secondary will be the
former on which the coil is wound.

• the short circuited secondary reduces
the effective inductance of the primary
- hence decay time is reduced

• in addition, the secondary should be in
thermal contact with the winding so that
it quenches other regions

Martin Wilson Lecture 3 slide34   Superconducting Magnets for Accelerators JUAS Feb 2006
LHC power supply circuit for one octant

circuit
breaker

• diodes allow the octant current to by-pass the magnet which has quenched
• circuit breaker reduces to octant current to zero with a time constant of 100 sec
• initial voltage across breaker = 2000V
• stored energy of the octant = 1.33GJ

Martin Wilson Lecture 3 slide35         Superconducting Magnets for Accelerators JUAS Feb 2006
Case study: LHC dipole protection
It's difficult! - the main challenges are:
1) Series connection of many magnets
• In each octant, 154 dipoles are connected in series. If one magnet quenches, the combined
inductance of the others will try to maintain the current. Result is that the stored energy of all 154
magnets will be fed into the magnet which has quenched  vaporization of that magnet!.
• Solution 1: put cold diodes across the terminals of each magnet. In normal operation, the diodes
do not conduct - so that the magnets all track accurately. At quench, the diodes of the quenched
magnet conduct so that the octant current by-passes that magnet.

• Solution 2: open a circuit breaker onto a dump resistor
(several tonnes) so that the current in the octant is
reduced to zero in ~ 100 secs.

2) High current density, high stored energy and long
length
• As a result of these factors, the individual magnets are
not self protecting. If they were to quench alone or
with the by-pass diode, they would still burn out.
• Solution 3: Quench heaters on top and bottom halves
of every magnet.

Martin Wilson Lecture 3 slide36        Superconducting Magnets for Accelerators JUAS Feb 2006
LHC quench-back heaters
• stainless steel foil 15mm x 25 mm glued to outer
surface of winding
• insulated by Kapton
• pulsed by capacitor 2 x 3.3 mF at 400 V = 500 J
• quench delay - at rated current = 30msec
- at 60% of rated current = 50msec
• copper plated 'stripes' to reduce resistance

Martin Wilson Lecture 3 slide37       Superconducting Magnets for Accelerators JUAS Feb 2006
Diodes to by-pass the main ring current

Installing the cold diode
package on the end of an
LHC dipole

Martin Wilson Lecture 3 slide38         Superconducting Magnets for Accelerators JUAS Feb 2006
Quenching: concluding remarks
• magnets store large amounts of energy - during a quench this energy gets dumped in the winding
 intense heating (J ~ fuse blowing)             possible death of magnet
• temperature rise and internal voltage can be calculated from the current decay time
• computer modelling of the quench process gives an estimate of decay time
– but must decide where the quench starts
• if temperature rise is too much, must use a protection scheme
• active quench protection schemes use quench heaters or an external circuit breaker
- need a quench detection circuit which must reject L dI / dt and be 100% reliable
• passive quench protection schemes are less effective because V grows so slowly
- but are 100% reliable
• protection of accelerator magnets is made more difficult by series connection
- all the other magnets feed their energy into the one that quenches
• for accelerator magnets use by-pass diodes and quench heaters
• remember the quench when designing the magnet insulation

always do the quench calculations before testing the magnet 

Martin Wilson Lecture 3 slide39       Superconducting Magnets for Accelerators JUAS Feb 2006

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