Dynamic behaviour of the S2C2 magnetic circuit

Report
Dynamic behavior of the S2C2 magnetic circuit
FFAG13 September 2013
Wiel Kleeven
The New IBA Single Room Proton Therapy Solution: ProteusONE
High quality PBS cancer treatment: compact and affordable
Synchrocyclotron with
superconducting coil:
S2C2
New Compact Gantry for
pencil beam scanning
Patient treatment room
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S2C2 overview
General system layout and parameters

A separate oral contribution on the field
mapping of the S2C2 will be given by Vincent
Nuttens (TU4PB01)

Several contributions can be found on the
ECPM2012-website
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Overview
Some items to be adressed
1.
2.
3.
4.
5.
6.
7.
8.
9.
Goal of the calculations
Different ways to model the dynamic properties of the magnet
What about the self-inductance of a non-linear magnet
Magnet load line and the critical surface of the super-conductor
Transient solver: eddy current losses and AC losses
A comparison with measurements
Study of full ramp-up/ramp-down cycles
Temperature dependence of material properties
A multi-physics approach and a qualitative quench model
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Efforts to learn more on the superconducting magnet
Coil and cryostat designed and manufactured by the Italian company ASG
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For the coming years, the proteus®one and as part of that, the S2C2, will be the
number®one workhorse for IBA
Succes of this project is essential for the future of IBA
A broad understanding is needed to continuously improve and develop this new system
The S2C2 is the first superconducting cyclotron made by IBA.
The superconducting coil was for a large part designed by ASG but of course by taking
into account the iron design made by IBA/AIMA. This was an interactive process
For us many things have to be learned, regarding the special features of this machine.
Some items under study now, or to be studied soon are:
1.
Fast warm up of the coil for maintenance
2.
Cold swap of cryocoolers for maintenance
The present study on the dynamics of the magnet must be seen as a learning-process
and any feedback of this workshop is very welcome
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Different models for the S2C2 magnetic circuit
1.
2.
3.
4.
5.
Opera2D/Opera3D static solver
Opera2D transient solver
Opera2D transient solver coupled to an external circuit
Semi-analytical solution of a lumped-element circuit model
Multi-physics solution of a lumped element circuit with temperaturedependent properties
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Magnetic circuit-modeling
OPERA3D full model with many details
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Long and tedious optimization process
Yoke iron strongly saturated
Influence of external iron systems on the
internal magnetic field
Stray-field => shielding of rotco and
cryocoolers
pole gap < => extraction system optimization
Influence of yoke penetrations
Median plane errors
Magnetic forces
ITERATIVE PROCESS WITH STRONG
INTERACTION TO BEAM SIMULATIONS
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The static Opera2D model
What information can we obtain
The magnet load line with respect to the superconductor critical
surface
1.
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Magnetic field distribution on the coil
Maximum field on the coil vs main coil current
Compare with critical currents at different temperature
The static self-inductance of the magnet
2.
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From stored energy
From flux-linking
The dynamic self-inductance of the magnet
3.
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Essential for non-linear systems like S2C2
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What do we get from Opera2D static solver
Load line relative to critical surface
maximum coil field
Magnet load line and
critical currents (from ASG)
S2C2 Field in the center and maximum field on the coil
7
Magnetic field (Tesla)
maximum coil
field during
ramp up
B_tot_center
6
B_iron_center
B_max_coil
5
4
3
2
windings/coil=3145
1
0
0
100
200
300
400
500
PSU current (Amps)
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600
700
800
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The static self-inductance of the magnet
The static self-inductance of the magnet
1.
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From the stored energy:
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From flux-linking:
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1
 = 2L 2
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Flux for a single wire in the coil:
 = 2
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Relation with vector potential:
 =

Total flux over coil:
 =

Self of one coil from flux-linking:
=

  
0

  
0
2

2

()
()
 
 
2nd method allows to find difference between upper and lower coil
Can be calculated directly in Opera2D
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Self-inductance from stored energy
Calculated with Opera2D static solver
S2C2 Stored energy and self-inductance
400
14
stored energy
350
12
static self
300
10
8
200
6
150
4
100
2
50
0
00
0
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250
windings/coil=3145
100
200
300
400
500
PSU current (Amps)
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600
700
800
Self (Henri)
stored energy (MJ)
16
Static self from flux-linking
Asymmetry may induce a quench? => probably not; DV=0.3 mV is too small
Introduces a voltage
difference between upper and
lower coil during ramp
Small vertical symmetry
in the model
Asymmetry in self-inductance of upper and lower coil
10
400
L(upper coil)-L(lower coil)
self
320
windings/coil=3145
6
240
0.3 mV
4
160
2
80
0
0
0
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100
200
300
400
500
PSU current (Amps)
600
700
800
Ltot (Henri)
Lup-Llow (mH)
8
What do we get from the 2D transient solver?
Eddy currents and related losses
Losses
Current density profiles
Losses in former, cryostat walls and yoke iron during a ramp
1.8
1.6
ramp-rate=2.7 Amps/min
1.4
former
Losses (Watt)
1.2
iron yoke
1.0
cryo-walls
0.8
0.6
0.4
0.2
0.0
0
Apply a constant ramp rate of
2.7 Amps/min to the coils
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50
100
Magnet current (Amps)
150
200
Eddy current losses
during ramp up and quench
During ramp-up
1.
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Eddy current losses in the former (max about 1.5 W) are important
because they contribute to the heat-balance
Losses in iron and cryostat walls are (of course) negligible
During a quench
2.
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When current decay curve is known, losses in former, iron and cryostat
walls can be calculated with OPERA2D transient solver
In the former: up to 15 kWatt
In the iron: up to 8 kWatt
The yoke losses help to protect the coil
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Opera2d transient solver coupled to external circuit
PSU drive programmed as in real live
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Cyclotron `impedance´is
calculated in real time by the
transient solver
Circuit currents are calculated in
real time by the Opera2D-circuit
solver
Allows to study full dynamic
behaviour of the magnetic circuit
during ramp up
Quench study is of qualitative
value only and has not been
done in Opera2D
The full ramp-up/ramp-down cycle
Default PSU-ramping for the S2C2
Used in the OPERA2D external circuit
simulations
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A full ramp-up and ramp-down cycle
Coil current compared to dump current
coil
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Dump (x10)
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It is seen that for a given
PSU current the magnetic
field in the cyclotron is
different for ramp-up as
compared to ramp-down
This is due to the fact the
dump-current changes sign
when ramping down
Higher coil currents in down
ramp
Tierod-forces during ramp-up and ramp-down
Seems to be in agreement with previous slide
60
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-10
50
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-20
40
Fx
-30
30
Fy
total
-40
Larger forces during down ramp
However:
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total (kN)
Fx,Fy (kN)
Horizontal forces on cold mass (040613)
0
20
-50
10
-60

0
200
300
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400
500
PSU-current (Amps)
600
700
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Current split between dump
and coil can not explain
completely the difference in
forces
iron hysteresis also seems to
play an important role
AC losses during ramp-up
From Martin Wilson course on superconducting magnets
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Hysteresis losses (W/m3)
2

 = 
 ()
3

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Coupling losses (W/m3)

( )2 
 =   ( )2
 2
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Tool developed in Opera2D-Transient
solver that integrates above
expressions in coil area
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Jc(B)
df
lsup
lwire
rt
p
dB/dt
=> critical current density
=> filament diameter
=> fraction of NbTi material
=> fraction of wire in channel
=> resitivity across wire
=> pitch of the wire
=> B-time derivative in coil
Critical surface => Bottura formula
Needed for AC losses calculation
Bottura formula
0
 =  (1 − ) (1 −   )


 =  (reduced temperature)
0

2 ()
=
(reduced field)
critical field at zero current
2  = 20 1 −  
a,b,g,C0 => fitting coefficients
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Critical surface => Bottura formula (2)
Critical surface at T=4 K (Bottura-formula)
Critical field as function of temperatue at zero current
(Bottura)
7
16
Normalized to unity at 5
Tesla/4.2 K
5
Spencer
Somerkoski
critical field (Tesla)
Critical current (normalized)
6
Green
4
Morgan
Hudson
3
2
1
Spencer
14
Somerkoski
12
Green
Morgan
10
Hudson
8
6
4
2
0
0
0
2
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4
6
8
Magnetic field (Tesla)
10
0
12
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1
2
3
4
5
6
Temperature (K)
7
8
9
10
Critical surface => S2C2 wire
Critical surface of S2C2 wire (3500 Amps @ 5Tesla/4.2 K)
18000
Critical current (normalized)
16000
T=3 K
14000
T=4K
12000
T=5 K
10000
T=6 K
8000
T=7 K
6000
4000
2000
0
0
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2
4
6
8
Magnetic field (Tesla)
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10
12
14
AC losses obtained with OPER2D transient solver
Initial results => maybe can be improved
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Hysteresis losses
somewhat larger than
eddy current losses
Coupling losses very
small
A lumped element model of the circuit
Turns out to give very good predictions
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Primary circuit
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  −  +  
2 −  

 
=
 
1

 1 + 2 (1 +   ) 



SOLVED IN EXCEL
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Secondary circuit
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PSU
Coil self-inductance
Coil resistance (only with quench)
Dump resistor
Former self-inductance
Former resistance
Perfect mutual coupling (k=1)
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Ideal transformer
Compare both models with experiment
Voltage on the terminals of the coils during ramp-up
Blue: measured
Black:OPER2D transient-circuit
model
Red: analytical lumped element
model
• Perfect match with
OPERA2D
• Not a good match with
lumped element model
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The concept of dynamic self-inductance
Important for non-linear magnets
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Definition of self-inductance:  = 
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Faraday’s law:
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Combine:  =   =   +
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  =
=



 

 
  +    =   (1 +   )
For a non-linear system the dynamic self must be used in lumped
element circuit simulations
 
 = 1 +   
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S2C2 self-inductance
A large difference between static and dynamic self
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Compare both models with experiment
Voltage on the terminals of the coils during ramp-up
Blue: measured
Black:OPER2D transient-circuit
model
Red: analytical lumped element
model with static self
Green: analytical lumped
element with dynamic self
An almost perfect
match is obtained
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Compare both circuit-models
Resistive losses in the former during ramp-up
Blue:OPER2D transient-circuit
model
Red: analytical lumped element
model
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Very good
agreement
between both
models
Further applications of lumped element model
Introduce a kind of « multiphysics »
Since this simple model works so well: can
we push it a little bit further?
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Resistors in model become temperature-dependent
Introduce additional equations for temperature change
() 2
 ()
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R(T) => resistance =>   =
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r(T) => resistivity
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Cv(T) => specific heat
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=
ℎ 
= ℎ ℎ
- 30 -
  

Specific heat of copper and aluminium
Very accurate fitting is possible

=  +  +  2
+ ⋯ +  8
 = log()
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Electrical resistivity of copper and aluminium
Same kind of fitting is possible
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A qualitative model for quench behavior
Based on (« multi-physics ») lumped element model
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Five different zones with four different temperatures in the cold mass
Upper coil superconducting zone (T0)
Upper coil resistive zone heated by resistive loss (T1)
1.
2.
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Resistive former heated by eddy current losses (T2)
Lower coil superconducting zone (T0)
Lower coil resistive zone heated by resistive loss (T3)
3.
4.
5.
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expanding due to longitudinal and transverse quench propagation
expanding due to longitudinal and transverse quench propagation
Start quench in upper coil
Lower coil will quench when former temperature above critical
temperature
ADIABATIC APPROXIMATION => no heat exchange between zones
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Model for quench propagation
From Wilson course
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Introduce the fraction f=fl*ft of the coil that has become resistive
1.
fl => Longitudinal propagation (fast  10 m/sec):


0 0
=  ⇒  =

  − 0
2.
ft =>Transverse propagation (slow  20 cm/sec):

=  ⇒  = 

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J => current density
G => mass density
Cv => specific heat
q0 => base temperature
qt => contact temperature
L0 => Lorentz number
Maximum temperature in the coil
Occurs at position where the quench started
Resistive loss per m3 equals increase of enthalpy per m3
2     =   
 2 
=


Where J is current density and g is mass density
Allows to calculate Tmax also from a measured decay curve
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Solution of quench module in Excel
Several differential equations are integrated in parallel
1.
2.
3.
4.
5.
6.
7.
8.
1 equation for the circuit current (slide 24)
3 equations for the average temperatures in resistive zone of both coils
and in the coil former (slide 30)
1 equation for the maximum temperature in the coil (slide 35)
2 equations for the longitudinal and transverse quench propagation in
the upper coil (slide 34)
2 equations for the longitudinal and transverse quench propagation in
the lower coil (slide 34)
Dynamic self is fitted as function of coil current
Material properties are fitted as function of temperature
All circuit properties (currents,voltages,resistances,losses) are obtained
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Current decay and quench propagation
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
Icoil
upper coil fraction
200
0.10
lower coil fraction
100
0.05
0
0.00
0
20
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40
60
Time after quench (sec)
80
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fraction of coil that is quenched (-)
Main coil current (Amps)
Main coil current decay and quench propagation
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After 50 seconds main
coil current already
reduced with a factor
10
At that time, about 25%
of both coils have
become resistive
Cold mass temperatures during the quench
Lower coil quenches about 0.1 seconds later
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Tmax  170 K
Tcoil  120 K
Tform  40 K
Ohmic losses during the quench
Iron losses may be obtained from Opera2D transient solver
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Voltages during the quench
Large internal voltages in resistive zones may occur
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Conclusions
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Many things have to be learned; this is only a start on one aspect
For learning we have to start doing
For example study of the quench problem will force us to learn:
1.
2.
3.
4.
5.
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More about material properties
More about heat transport in the cold mass
More about mechanical/thermal stress in the coldmass
Multi-physics approach
….
A precise quench study needs to be done with 3D finite element codes
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Quench model in Opera3D?
Comsol ?
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