3D Simulation of Transient Effects
in Accelerator Magnets
Herbert De Gersem
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 1
Cooperation DESY - TEMF
current research topics
• eigenvalue calculations
• resistive wakefield calculations
• photo-emission studies
brainstorm on further cooperation topics
• new cavity structures
• simulation of multipacting
• simulation of wakefield acceleration
• simulation of transient effects in accelerator magnets
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 2
Accelerator magnets
•
•
•
•
complicated geometries + production tolerances
3D effects (fringing, eddy currents)
multi-physics (cryogenics, deformation)
multi-scale models
(windings, laminations)
• transients (e.g. remanence)
• materials ...
SIS100 magnet, GSI
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 3
Materials
turning point
reversible area
B(t)
major loop
H(t)
minor loop
critical current density (A/mm2)
• ferromagnetic materials
(nonlinear, hysteretic, magnetostriction)
• superconducting materials
(thermal & magnetic stability, persistent currents)
• composites (homogenisation)
• windings (homogenisation)
• uncertainties
12000
10000
NbTi
8000
1660 A/mm2
6000
4000
0 A/mm2
2000
0
0
0
2
4
2
4
magnetic
flux density (T)
5 T6
6 4.8 K
8
10
8
12
14
10
temperature (K)
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 4
Discretisation in space
differential equation:
r
r
∂A r
∇ × ν∇ × A + σ
= Js
∂t
(
spatial discretisation
edge finite elements
(curl-conforming)
)
r r
) r
A ≈ AFE = ∑ a j w j
j
r
wj
temporal discretisation
Runge-Kutta
discrete system:
)
( Kν + α Mσ ) ak +1 = RHS
B/T
) ))
da
)
= js
semi-discrete system: Kν a + Mσ
dt
∆t
time / s
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 5
GSI SIS100 magnet
40
eddy-current losses over
one cycle for different
stacking factors γ
35
13 J
30
10 J
25
20
B/T
power losses / W
pk
γ pk = 93%
γ pk = 96%
γ pk = 98%
15
∆t
10
8J
time / s
5
0
0
0.25
S. Koch, J. Trommler, T. Weiland, TU Darmstadt
0.50
0.75 1.00
time / s
1.25
1.50
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 6
Computation effort
0
relative error
10
solution of 110 x 4 = 440
linear systems of equations
r tv,(0)
wj
4.4 h @ 132 CPUs
-1
10
r
wtv,(1)
j
-2
10
r
7.3 h @ 72 CPUs
-3
10
10 4
FE, wtv,(0)
j
r tv,(1)
FE, w j
10 5
10 6
10 7
number of dofs
+ 2 per face
10 8
S. Koch, J. Trommler, T. Weiland, TU Darmstadt, 2009
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 7
Stern-Gerlach magnet
field homogeneity (original geometry)
field homogeneity (optimised geometry)
B. Masschaele, H. De Gersem (KU Leuven)
A. Pels, J. Corno, Z. Bontinck, S. Schöps, (TU Darmstadt)
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 8
Magnet simulation @ TEMF
Competence
• 3D transient FE solvers
• material models
• accurate post-processing (multipoles)
• uncertainty quantification and sensitivity analysis
Cooperation
• S-DALINAC magnets
• GSI magnets
• cooperation with CERN on the modelling
of quench propagation
18 februari 2015 | TU Darmstadt | Fachbereich 18 | Institut für Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Herbert De Gersem | 9

Magnet design at the ESRF