Transcript 11x - CERN Indico

Unit 11
Protection
Ezio Todesco
European Organization for Nuclear Research (CERN)
Based on the USPAS course of Helene Felice, LNBL, now at
CEA, Saclay France
E. Todesco, Milano Bicocca January-February 2016
CONTENTS
1. Heat capacity versus Joule heating
2. Energy extraction with dump resistor
3. Quench heaters
4. Scaling laws
5. Quench propagation and detection time
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 2
HEAT CAPACITY VS JOULE HEATING
After quench, one has Joule heating
power converter is switched off
magnet has growing resistance depending on quench propagation
dump maybe included in the circuit
we have an RL circuit
We assume that the heat stays where it is generated (adiabatic)
Joule heating gives power heating the coil
The resistance depends on the coil temperature, highly nonlinear
problem
Integrating we have
The coil will reach the temperature Tmax
But the unknown is j(t)
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 3
HEAT CAPACITY VS JOULE HEATING
What is a safe Tmax that can be reached in the coil?
Usually one does not want to go much beyond room temperature 30 C,
at most 80 C (350 K)
Main reasons
For Nb-Ti damaging of insulation above 250 C (melts)
For all cases this very rapid (in fraction of second) heating induces local
thermal stresses that can damage the cable
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 4
HEAT CAPACITY VS JOULE HEATING
Let us consider some orders of magnitude
Below you see a typical plot of the right hand side integral for a
typical Nb-Ti cable with half of copper in the cross-section
The integral makes something of the order of 1017 J/W/m4
Let us assume the time decay is very rapid, how much time to react?
So we can see that having 500 A/mm2, we can stay a time
0.5×1017/(5×108)2 = 0.2 s at that current
I
I0
t
R
= L/R
tdet
E. Todesco, Milano Bicocca January-February 2016
t
Unit 9 - 5
HEAT CAPACITY VS JOULE HEATING
The right part of the integral is a intensive property of the
cable
Let us go to extensive properties
I: current in the cable
rcu: copper resistivity
n: fraction of copper
cpave: volumetric specific heat
A: cable surface
Let us call the right hand side gamma
This has a physical dimension of a square of current times time (A2 s)
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 6
HEAT CAPACITY VS JOULE HEATING
The left hand term is much more difficult
This is a L R circuit whose time constants is L/R
One can put in series an external resistor
If this resistor is much larger than the resistance of the magnet, the
computation is easy
We will see it in the next section
Otherwise …
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 7
HEAT CAPACITY VS JOULE HEATING
Otherwise one has to go for numerical methods
Integration by steps in time and space, very careful since fine
(adaptive) grid has to be used
In the initial part, specific heat very small, time step should be of the
order of 0.1 ms
Simplified case, assuming that all magnet is resistive at the
same temperature, we see explicitly how to solve
In this case the coil will go at the same temperature
… but only at first order since resistivity depends on magnetic field
so parts of the coil at lower field will reach lower temperatures
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 8
HEAT CAPACITY VS JOULE HEATING
In the community one usually defines the MIITS of the cable
This is the capital we can spend
Then we consider the a perfect protection system able to
quench all magnet instantaneously at time 0
The current will decay, circuit L R where the resistance varies since
the current is heating with the Joule effect
Gq are the MIITS of such an hypotetical quench



Gq   I q (t ) dt
2
0
E. Todesco, Milano Bicocca January-February 2016
Protection in magnet design - 9
CONTENTS
1. Heat capacity versus Joule heating
2. Energy extraction with dump resistor
3. Quench heaters
4. Scaling laws
5. Quench propagation and detection time
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 10
ENERGY EXTRACTION
To decrease the current as soon as possible, one can
Switch off power converter
Insert a resistor Re on the circuit
One has a LR circuit with time constant L/R
Neglecting the magnet resistance, the time constant is t=L/Re
Integration gives
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 11
ENERGY EXTRACTION
So increasing the dump resistor one can reduce the quench
integral
There is a severe limit is this strategy: the voltage induced on the
magnet at the beginning of the discharge
This voltage is usually limited to about 1 kV – due to the maximum
voltage that can be withstand by insulation
Since the inductance is proportional to the magnet length, for long
magnets the inductance becomes too large and one cannot satisfy the
above equation
One has to go for another strategy, independent of the magnet
length
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 12
CONTENTS
1. Heat capacity versus Joule heating
2. Energy extraction with dump resistor
3. Quench heaters
4. Scaling laws
4. Quench propagation and detection time
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 13
QUENCH HEATERS
The idea of quench heaters is to quench rapidly all the
magnet so that the resistance is growing rapidly
The energy of the magnet is dumped on the coil itself, but not only
on the small portion that is quenching
Quench heaters are strips of stainless steel where an impulse of
current is put as soon as the quench is detected
Strips heat thanks to Joule heating, and since they are glused on the
coil they turns all the coil resistive
The reaction time that can be obtained is of the order of 10-50 ms
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 14
QUENCH HEATERS
How much time needed to quench a magnet?
Obviously, the larger the margin the longer the time
So at lower current one needs more time to quench
But at lower current the current density is lower …
Limit to the heater delay is the thin strip of insulation that avoids
electrical contact between the coil and the heaters
Usually a good insulator is also a bad thermal bridge
70
Cover 3 cm
3rd turn l
fie d
PH delay (ms)
60
50
40
Cover 6 cm
7th turn l
fie d
30
20
10
HQ01e - CERN 4.4 K
0
0
E. Todesco, Milano Bicocca January-February 2016
20
40
60
I/Iss (%)
80
100
Heaters delay vs model [T. Salmi, H. Felice]
Unit 9 - 15
TIME MARGIN
Let us assume that after a time Tq, all the magnet is
quenched, at the critical temperature
And let us assume that Iq(t) is the current decay in a magnet
quenching « on itself »
This can be estimated through numerical codes, and the quench integral
can be computed
It is a property of the magnet design
How long we can survive at maximal current ?
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 16
TIME MARGIN
Tq is the time margin for protection
This gives the time required to react to the quench and to spread all
the quench through the quench heaters before the magnet reaches
Tmax
Order of magnitude:
For Nb-Ti high field magnets the magnet design aims at having around
100 ms
For Nb3Sn high field magnets we try to go towards 50 ms
Less becomes impossible ..
I will show why
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 17
CONTENTS
1. Heat capacity versus Joule heating
2. Energy extraction with dump resistor
3. Quench heaters
4. Scaling laws
4. Quench propagation and detection time
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 18
SCALING LAWS
1. A very old discussion between magnet designers:
Large cable and large current but small inductance or viceversa ?
The same magnet, with same field and same energy, can be built
with a large or a small cable
w  w’=2w
A  A’=2A
Io  Io’=2Io
L  L’=L/4
U  U’=U
Re  Re’=Re/2
G  G’= 4G
LI2o/2Re  2 L’I’2o/2R’e
So if we extract on a dump resistor, increasing the current and the cable
size we manage to protect better
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 19
SCALING LAWS
2. The energy extraction on a dump does not work for long
magnets:
A longer and longer magnet will not be protected by a dump resistor
Consider a magnet with the same cable but with double length
w  w’=w
A  A’=A
Io  Io’=Io
L  L’=2L
U  U’=2U
Re  Re’=Re
G  G’= G
LI2o/2Re  2 L’I’2o/2R’e
So at a certain length the energy extraction becomes not effective
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 20
SCALING LAWS
3. The quench heater strategy works for any length
Consider a magnet with the same cable but with double length
w  w’=w
A  A’=A
Io  Io’=Io
L  L’=2L
U  U’=2U
Rm  Rm’=2Rm
G  G’= G
LI2o/2Rm  L’I’2o/2R’m
This happens because we now dump on the magnet, and a longer magnet
has also a larger resistance
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 21
SCALING LAWS
4. The quench heater strategy does not depend on small or
large inductance
Consider a magnet with the double cable width
w  w’=2w
A  A’=2A
Io  Io’=2Io
L  L’=L/4
U  U’=U
Rm  Rm’=4Rm
G  G’= 4G
LI2o/2Re 4 L’I’2o/2R’e
The small or large inductance becomes important for other aspects
(inductive voltages) not treated here
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 22
SCALING LAWS
Consider a magnet with the double cable width
w  w’=2w
A  A’=2A
Io  Io’=2Io
L  L’=L/4
U  U’=U
Rm  Rm’=4Rm
G  G’= 4G
LI2o/2Re 4 L’I’2o/2R’e
The small or large inductance becomes important for other aspects
(inductive voltages) not treated here
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 23
ANALYTICAL ESTIMATE OF TIME MARGIN
One can work out an analytical estimate of the time margin
Copper fraction
strand current density
strand enthalpy
stored energy/strand volume
Main message is
Since the coil takes the heat, the energy density on the coil should
not be larger than the enthalpy from operational temperature to Tmax
(300 K), that is about 0.5 J/mm3
As usual, there is a dependence on j 2: larger current densities
reduce the margin with a square
Once more we see a barrier for high current densities
E. Todesco, Milano Bicocca January-February 2016
Protection in magnet design - 24
ANALYTICAL ESTIMATE OF TIME MARGIN
Strand energy density (J/mm3)
Ud
Case of some magnets
0.20
FrescaII
MQXF
(200 ms)
0.15
(33 ms)
HD2
(80 ms)
HQ (23 ms)
11 T
(33 ms)
LHC MB (220/110 ms)
0.10
0.05
TQ
(17 ms)
MQXC (160/60 ms)
0.00
0
400
800
Strand current density (A/mm2)
jo
1200
Energy density Nb-Ti 0.07 J/mm3 (1/10 of Cpave)
Energy density Nb3Sn 0.10-0.15 J/mm3 (up to 1/4 of Cpave)
E. Todesco, Milano Bicocca January-February 2016
Protection in magnet design - 25
CONTENTS
1. Heat capacity versus Joule heating
2. Energy extraction with dump resistor
3. Quench heaters
4. Scaling laws
5. Quench propagation and detection time
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 26
QUENCH PROPAGATION AND TIME MARGIN
Why do we need a time margin of at least 50 ms ?
10-20 ms to quench the coil through heaters
But there are other contributions
To detect a quench one measures the voltage generated by the
resistance
Voltage threshold are typically 100 mV, and it takes about 5-10 ms for
the quench propagation to generate this voltage
There is also the time necessary to open the switch, that can be of the
order of a few ms
Studies are ongoing to reduce this limit towards 25 ms
Innovative method: CLIQ, patent at CERN (G. Kirby, E. Ravaioli)
One discharges a capacitor in the coil, the dB/dt induces heating tha
quenches the coil
E. Todesco, Milano Bicocca January-February 2016
Protection in magnet design - 27
SUMMARY
Quench protection consisits in getting rid of the current as
soon as the quench is detected
This should be done within 0.3 – 0.5 ms for typicl accelerator
magnets
Since the inductance is given one has to work on the increase
resistance
External dump resistor is valid only for small magnets
Dumping the energy on the coil itself is limited by the coil enthalpy
The quench velocity is small, and to the quench propagation has to be
helped by heaters to quench all the coil as soon as possible to increase
the resistance
This can be done in 10-20 ms
Protection sets phyisical limits on current density
That is the coil enthaply must be much larger than the energ density on
the coil
If the coil is too compact, it cannot take the energy of the magnet
E. Todesco, Milano Bicocca January-February 2016
Unit 9 - 28