Simulation of the fast dump process of the ATLAS toroids
Gabriella Rolando
Technical Student @ ATLAS Magnet team
1
Outline
• Introduction
• Fast dump of the Barrel Toroid (stand alone)
• BT energy distribution
• Fast dump of End Cap Toroid A (stand alone)
• ECTA energy distribution
• Fast dump of the entire ATLAS toroids system (ABC)
• ABC energy distribution
2
The Barrel Toroid
• 8 racetrack coils 25 x 5 m
• operating current = 20.5 kA
• stored energy = 1080 MJ
• peak field = 3.85 T
• operating temperature = 4.6 K
BT conductor
3
The End Cap Toroids
• 8 racetrack coils 4.5 x 4 m
• operating current = 20.5 kA
• stored energy = 229 MJ
• peak field = 4.1 T
• operating temperature = 4.6 K
Keystone boxes
4
BT: electric model
dI
L ⋅ + I ⋅ ( R + Rcoils ) + VD = 0
dt
L
BT self inductance
R
cable & dump unit resistors resistance
Rcoils BT total resistance
VD voltage drop across the diodes
Thermal shield < 0.01%
∞
2
E = ∫ (M
0
dI
1
) ⋅ dt
dt
R
M
mutual inductance
R
element resistance
Vacuum vessel
< 0.01%
Casing ~ 0.7%
5
BT: thermal model
A
Q = k ⋅ ⋅ ΔT
l
Q thermal energy
k
thermal conductivity
A
heat exchange surface
l
heat diffusion length
bladders
ΔT temperature difference
After ~ 2 min
6
BT: Al resistivity
The main factors that determine the Al resistivity are:
• purity grade of the material
• temperature
• magnetic field
Average B ~ 1.8 T
7
BT: energy release due to the current redistribution
Current diffusion time constant
τ ~ few s
An accurate treatment of the problem implies the solution of
Maxwell’s equations
heat conduction and
diffusion equations
A alternative way has been followed that looks at the changing
magnetic field energy density between the beginning and end of the
process.
8
BT: energy release due to the current redistribution
B∝r
B∝
1
r
To calculate the energy release:
• B field energy density
E ~ 10 MJ
Tinitial ~ 21K
• conductor length (~ 60 km)
9
BT: simulation of a fast dump
Using Mathematica
1. Resistance of double pancakes
2. Current
3. Energy dissipation in coils
4. Energy transfer from coils to casing
5. Temperature increase
10
Electric analysis
• Discharge time ~ 180 s
• ΔI max ~ 7%
(t ~ 60 s)
• BT resistance
Rmax < 0.20 Ω
12
Thermal analysis /1
Temperature rise (200 s)
41
40
T (K)
39
calculated
38
Temperatures after 200 s from
the beginning of the dump
measured
37
36
35
1
2
3
4
5
6
7
8
Average difference 3%
coil number
13
Thermal analysis /2
At the end of the dump the temperature of the coils can be estimated
on the base of the energy dissipation in the double pancakes.
Vactive = Vtotal
dI
− L⋅
dt
∞
Ei = ∫ (VDPAi + VDPBi ) ⋅ Idt
Vactive= VDPi resistive voltage across double pancake
0
Vtotal total voltage across double pancake
Ei
H i (T ) =
m
T
L
DP inductance
dI/dt current derivative
Ei
coil energy dissipation
Hi
coil enthalpy
m
coil mass
14
Thermal analysis /2
Average difference
Tcalculated –Tmeasured = 1%
Tcalcualted –Tvoltage = 1%
In general:
• Tmeasured affected by restart of He flow
• Tcalculated influenced by
correctness of RRR
values
15
Energy dissipation
Energy dissipated in a coil
Ecoil = ∫ I ⋅Vactivedt
16
E = ∑ E DPi = 1047 MJ
Energy dissipated in BT
i =1
8.0E+07
7.5E+07
coil 1
coil 2
7.0E+07
Average coil dissipation
E(J)
coil 3
coil 4
6.5E+07
coil 5
131 MJ
coil 6
6.0E+07
coil 7
coil 8
5.5E+07
5.0E+07
500
1000
1500
2000
2500
3000
RRR
16
Energy distribution
Edump = − ∫ I ⋅Vtot = 32.5MJ
16
Ecoils = ∑ E DPi = 1047 MJ
i =1
Energy distribution in BT coils (dump from 20.5 kA)
Eexp = 1079.5MJ
Eth =
1 2
LI = 1080MJ
2
Unknown 1.6%
Al 27.7%
Casing 47.9%
Cu 2.5%
SC 2.5%
Dump 3.0%
Insulation 14.8%
17
ECT: electric model
dI
L ⋅ + I ⋅ ( R + Rcoils ) + VD = 0
dt
L
ECT A self inductance
R
cable & dump unit resistors resistance
Rcoils ECT A total resistance
VD voltage drop across the diodes
∞
2
dI
1
E = ∫ ( M ) ⋅ dt
dt
R
0
M
mutual inductance
R
element resistance
Casing ~ 0.7%
18
ECT: thermal model
Al alloy central plate
After ~1 min
19
ECT: Al resistivity & initial conditions
Average magnetic field on ECT
conductor
Energy release to the conductor:
• B field energy density
• conductor length (~ 13 km)
B=2T
E ~ 1.3 MJ
Tinitial ~ 19 K
20
Electric analysis
• Discharge time ~ 90 s
• ΔI max ~ 26%
(t ~ 63 s)
• higher difference due to
keystone boxes
• ECT A resistance
Rmax < 70 mΩ
21
Thermal analysis /1
Temperature rise (120s)
44
43
42
T (K)
calculated
measured
41
Temperatures after 120 s from
the beginning of the dump
40
39
1
2
3
4
5
coil number
6
7
8
Average difference 3%
22
Thermal analysis /2
Average difference
Tcalculated –Tmeasured = 3.5%
Tcalculated –Tvoltage = 1.3%
In general:
• Tmeasured influenced by
keystone boxes
• Tmeasured affected by restart of He flow
• Tcalculated influenced by
correctness of RRR values
23
Energy dissipation
Energy dissipated in ECT A
Average coil dissipation
16
E = ∑ E DPi = 219.7 MJ
27.5 MJ
i =1
1.7E+07
1.6E+07
coil 1
1.5E+07
coil 2
coil 3
H (J)
1.4E+07
coil 4
coil 5
1.3E+07
coil 6
coil 7
1.2E+07
coil 8
1.1E+07
1.0E+07
500
1000
1500
2000
2500
3000
RRR
24
Energy distribution
16
Energy distribution in ECT A coils
(dump from
20.5 kA)
Dump
Insulation
3%
4%
i =1
Edump = − ∫ I ⋅ Vtot = 8.8MJ
Unknown
15%
SC
2%
Al
11%
Casing
63%
Ecoils = ∑ E DPi = 219.7 MJ
Eexp = 228.5MJ
1 2
Eth = LI = 229MJ
2
Cu
2%
Missing energy ~ 15%
E keystone boxes ~ 11.4%
Missing energy ~3.8%
25
ABC: electric model
Current equations
with
26
ECT: electric analysis
• R ECTA max ~ 75 mΩ
• R ECTA max in ABC configuration
~ 10 mΩ higher
ECT A resistance
ECT C resistance
• R ECTC max < 70 mΩ
• R ECTA max > R ECTC max
because of the lower average
RRR of the double pancakes
27
BT: thermal analysis
Temperature comparison after 200
s from the beginning of the dump
Temperature rise (200 s)
42
40
Average difference 6% (
calculated
measured
36
)
34
32
30
1
2
3
4
5
6
7
8
Final temperatures comparison
coil number
61
60
coil 1
59
coil 2
58
Average difference
T (K)
T (K)
38
coil 3
coil 4
57
coil 5
coil 6
56
coil 7
Tcalculated –Tmeasured = 2% ( )
55
Tcalcualted –Tvoltage = 1% ( = )
53
coil 8
54
calculated
measured
from active voltage
28
ECT A: thermal analysis
Temperature rise (120 s)
45
Average difference
44
Tcalculated –Tmeasured = 4% ( = )
T (K)
43
42
calculated
measured
41
Tcalculated –Tvoltage = 2% ( )
40
39
38
1
2
3
4
5
6
7
8
Final temperatures comparison
coil number
54
52
Average difference 3.6% ( = )
coil 2
50
coil 3
T (K)
Temperature comparison after
120 s from the beginning of the
dump
coil 1
coil 4
48
coil 5
coil 6
46
coil 7
coil 8
44
42
calculated
measured
from active voltage
29
ECT C: thermal analysis
Temperature rise (120 s)
Temperature comparison after 120 s
from the beginning of the dump
43
42.5
Average difference 1%
calculated
41.5
measured
41
40.5
40
1
2
3
4
5
6
7
8
coil number
Final temperature comparison
54
52
Average difference
Tcalculated –Tmeasured = 6%
Tcalculated –Tvoltage = 2.5%
coil 1
50
T (K)
T (K)
42
coil 2
coil 3
48
coil 4
coil 5
46
coil 6
coil 7
44
coil 8
42
40
simulated
measured
from active voltage
30
Energy distribution
Energy distribution in the coils
(dump from 20.5 kA)
• casings > 50%
• BT Al stabilizer ~ 20 %
• BT insulation ~10%
• remaining elements each < 2%
• 5% initial energy missing
Keystone boxes
contribution
E keystone boxes = 3.8%
Eth =
1
( LBT + 2 ⋅ LECT + 4 ⋅ M ) I 2 = 1571.7 MJ
2
Missing energy reduces to 1.2%
31
Conclusions
• Simulation of the fast dump of the
single toroids from the electrical and
thermal point of view
• Results have been validated through
the comparison with experimental data
• The simulation is able to describe behavior of the system with a quite
good level of accuracy (~ 5%)
• The models of the single magnets have been unified to simulate the fast
dump of the complete ATLAS toroid system
• The energy distribution inside the coils has been determined: while the
BT coils constitute an adiabatic system, the energy balance of the ECTs is
influenced by the keystone boxes
32