# Presentation: 102287

## Finite Element Calculations on Detailed 3D  models for the Superferric Main Magnets of the FAIR SIS100 Synchrotron 

- E. Fischer, GSI, Darmstadt, Germany
- R. Kurnyshov, Electroplant, Moskow, Russia
- P. Shcherbakov, IHEP, Protvino, Russia

- e.fischer@gsi.de

- Egbert Fischer, Planckstraße 1, 64291 Darmstadt, Germany

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Contents - references 

-  _methodical investigations:_
-   P. Shcherbakov, E.Fischer and R. Kurnyshov, “3D magnetic field and eddy loss calculations for iron dominated accelerator magnets using **ANSYS compared with results of noncomercial codes**”, **EPAC 2006**, WEPLS094
-  _comparison to experiments:_
-  E. Fischer et al.., “**3D** **transient process** calculations for fast cycling superferric accelerator magnet”, **MT-19**, THA07PO06
-  _application results_
-  E.Fischer et al., “Analysis of the superferric **quadrupole magnet** design for the SIS100 accelerator of the FAIR project”, **EPAC 2006**, WEPLS091
-  P. Shcherbakov, E.Fischer and R. Kurnyshov, “3D field computations for **main prototype m****agnets** of the SIS100 Accelerator of the FAIR”, **EPAC 2006**, WEPLS093
-  E.Fischer, R. Kurnyshov and P. Shcherbakov, “Analysis of the **Eddy Current Relaxation Time Effects** in the FAIR SIS 100 Main Magnets”  **ASC 2006**, 5LF04

## Introduction: New international accelerator complex

**Introduction: ****New international accelerator ****complex**

**Separators**
**Storage Rings**
**CR-complex**

** **SIS300** **

** ****SIS100 **

**Synchrotrons**

***GSI***

***FAIR***

**www.gsi.de  ****►**** **FAIR- Facility for Antiprotons and Ion Research

**provide:**
**High beam intensity**
**High beam energy  **
**High beam quality**

**for:**
**ions and antiprotons for experiments in nuclear, atomic and plasma physics**

## SIS100 Magnets                      I/II

- Nuclotron (JINR, Dubna, Russia)
- reference design

## SIS100 magnets R & D - initial design: 	II/II

- Iron dominated („window frame“- type ) superferric design
- Cold iron
- Maximum magnetic field: 2 T,  Ramp rate: 4 T/s
- Hollow superconducting cable, indirectly cooled
- Two-phase helium cooling

**Nuclotron Dipole**

## AC loss reduction - R&D phase: Models

**Nuclotron dipole inside cryostat: **
**1 - yoke end plate **
**2 - brackets**
**3 - coil end loop**
**4 - beam pipe **
**5 - helium headers**
**6 - suspension**
**7 - laminated yoke**

**Test measurements on magnet modifications **
** ****FEM calculations on detailed 3D-models**

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Computer Modeling: Motivation

- Superconducting iron dominated magnets in unconventional regime:   deep steel saturation at low temperature
- Only one *other* accelerator worldwide!
- Understand magnet behaviour
-  AC Loss generation
- Field quality DC / AC
- Aid R&D
- Choice of material (AC loss)
- Field quality  in 3D design
- Aid model / prototype development
- Study magnet behavior in the machine
- Powering history
- Relaxation effects
- Cycle effects

## Computer Modelling: Specs

-  Multiphysics
-  electrodynamic properties
-  magnetic field (yoke, aperture)
-  eddy currents
-  Lorentz forces
-  thermal properties
-  One mesh for all properties (per magnet model)
-  Parametrized models (if required)
-  limit human errors for different models
-  CAD interfaces for interaction with magnet designers

## Computer Tools: Pro Engineer

-  Model Creation	CAD system Pro Engineer
-  parametric model: but needs remeshing
-  material with properties
-  lamination, infinite resistance in z
-  end plates and brackets: low carbon steel / stainless steel   3D magnetic and electric properties
-  elliptical beam pipe and support structure
-  allows connecting different parts

## Computer Modelling: ANSYS  I /II

- Solver: ANSYSTM
- 3D
- Static / transient
- Edge Formulation: Edge elements are vectore finite elements, with the property that tangential component is continuous at the interface of the adjacent elements, but the normal component may jump. This is precisely the physical behaviour of the magnetic field strength H at material discontinuity.
- Higher accuracy than Magnetic Vector Potential
- Huge experience by one of the authors (R. Kurnyshov) for electromechanical and electrotechnological devices
-  recommended choice for devices with
- Different ferromagnetic material
- Arbitrary current coils

## Edge formulation for 3D transient analysis 

- Edge elements are vectore finite elements, with the property that tangential component is continuous at the interface of the adjacent elements, but the normal component may jump.
- This is precisely the physical behaviour of the magnetic field strength H at material discontinuity.
- Edge elements are therefore very much suitable for calculating the magnetic field directly. No calculation of  a potential is required.
- “Edge element analysis of magnetostatic and transient eddy current fields using H-formulations”
- C.Gaier and H. Haas, Vena, IEEE trans 0n Mag, vol. 31 no 3may 1995. pp1460

## Advantages of edge elements:

- First edge elements allow direct computation of the field of interes, be it the magnetic  field, or electric field, without any recourse to differentiation from some potential,
- Next, they do note impose on H or E more continuity than physics require: edge elements aproximations of H will have tangential continuity across material interfaces, but its normal component will not be forced to (unwanted) continuity by the nature of finite-element interpolants as may happen with some node-based elements.
- Finally, edge elements are well adapted to the coupling of finite elements (in the iron region) and boundary eelements (on the air-iron interface), which is the way to cope with the problem of far-field effects in open electromagnetic systems.
- “A rationale for “edge-elements” in 3D field computations”
- 	 A. Bossavit, IEEE trans on Mag, vol 24 no 1may 1988. pp74
- see also:  ANSYS manual

## Computer Modelling: ANSYS II /II

- Meshing
- Required accuracy in acceptable time
- Fourier coefficients for magnetic field
- Field specified to  500 ppm!
- One mesh for AC losses and harmonic
- Careful meshing of the 3D model- most important stage for successful computation

## Material Properties: Steel       I /III

- Different steels
- Lamination electrical silicon steel (4 T/s) (SI)
- Mechanical rigidity
- Brackets
- End plates
- Stainless Steel (SS),
-    Low Carbon Steel (LC)
- Lamination → packing factor

## Steels: magnetic properties

**Table:  Steels used in the accelerator magnets**
**rho**** in**** [**** ****mOhm.****m**** ] ****@**** ****4. 2 K, **
**M****s**** in [T] **(saturation magnetization)

## Material Properties: Steel       II/III

## Material Properties: Steel     III/III

- _For laminates tangential to the flux:_
- 	       μeff = fp · (μr - 1 )  + 1

- μr  - permeability of laminate
- fp = Wi / (Wi + Wa ) - packing factor
- Wi - thickness single laminate
- Wa - thickness  non-permeable material between the laminates

- _For laminates__ __normal to the flux:_
-       μeff = μr / ((μr - fp · (μr - 1)))

## Modelling Steel: xy, z

-  z , xy different for laminated magnets
- ANSYS: only one r(H)
-  xy  = r(H)
-  z
- fp  = 1 : r(H)
- fp  =< 1:  1 / (1 - fp) z = 15 – 50
-  z  nearly constant  1.5 - 1.7 T
- Impact of decreasing
-  permeability near 2 T → estimated

- Electrical Yoke steel 3414

## Longitudinal permeability

- Longitudinal permeability is practically constant up to B=1.5-1.7 T depending only on  packing factor
-  z(B) constant 1.5 – 1.7 T
-   z(B) non linear B > 1.7 T

## Hysteresis Computation

- Comparison with calorimetric measurements needs the knowledge of hysteresis loss in different parts.
- The small code has been developed:

-  Calculate Field in the each part (lamination, yoke, end plates)
-  Use formula
-  sum the individual parts

- e.g. SI steel : Qv(B) = 50.775 B3 – 67.169 B2 + 42.45 B  [W/m**3]

## Computational Effort

- one variant of transient process
- for full scaled detailed magnets
- 4 hours         simple models
- 50 hours       full length quadrupole

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Simplified model

- Verify approach
- 		triangular cycle 0 →  Imax / Bmax
- Comparison with other method calculations
- Comparison with the experimental data

## Slide 26

## Current cycle 

- Maximum current  - 4800 A
- Maximum central field 2.05 T (there is small non-linearity of field due to saturation)

## 4 cases of longitudinal permeability have been calculated

***        *****μ****Z**** = 15  ******** f****P**** = 0.94**
***        *****μ****Z**** = 25  ******** f****P**** = 0.96**
***        *****μ****Z**** = 50  ******** f****P**** = 0.98**
***      ****** *****μ****Z**** = μ****XY**** = μ****Z**** (B) ******** f****P**** = 1.**
***     *****μ****Z**** ****max=4000**

*** ***

## Dependence of eddy current power on time in laminated yoke μZ =15

## Eddy losses distribution along the yoke

***μ******r******(X,Y) ↔ original B(H) curve***
*** ******μ******r******(Z) = 15***

-  W / m

- for different t [s]

- losses in the magnet end

## Vectors of eddy current density in yoke

- (t=0.36 s, 1-st ramp) for μr(Z)=25, A/m2

## Vectors of  BZ in yoke vs time for μr(Z)=25, T

***Vectors of  B******Z****** in yoke vs time for ******μ******r******(Z)=25,****** T***

## Isosurfaces of eddy losses density in yoke

- t=0.52 s,  flat top
-  for μr(Z)=25, W/m3

## Isotropic case , ideal packing factor =1

- The case of fp=1 corresponds to isotropic magnetic properties,
-      when longitudinal permeability is equal to the plane one and has
-      strongly nonlinear character.
- This case has been studied separately from point of view relaxation time.

## fp=1: Time dependence of eddy current power

- Loss only during ramp up
- Eddy during ramp down inopposite direction cancel with eddies from ramp up

**Time averaged eddy losses (for a single cycle): ~15.93 W (J per cycle)**

## Results (comparison of eddy current loss with other code results and measured value)

- Summary of the calculations is shown in Figure: the P(t) dependencies of eddy current power together with B(t).
- Calculated results *12 W*,
- 	(other codes give  *19-23 W  for the same conditions*)
- Experimental *9-10 W*
*Good Agreement! *
- Difference explainable by not perfectly known parameters for different steel of the magnet

## Relaxation study for simplified yoke isotropic case

- First approach:

- Two cycles with different pauses
- Constant time of relaxation – 0.52 s [MT-19]

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Model for SIS 100

- SIS 100 models (Nuclotron based)
- Coil
- Large coil (Nuclotron)
- Small coil
- Laminated yoke
- With end slits
- Thick end plates
- Low carbon steel
- Stainless Steel
- Longitudinal brackets (LC)
- Low carbon steel
- Stainless Steel

## Example for comparison with measured value

-  Endplate and brackets 	low carbon steel
-  standard triangular cycle 4 T/s
-  yoke lamination packing factor 0.97 – 0.98
-  μr(Z) = 25
-  standard current impulse (triangular cycle)

## FE mesh (“active” parts)

## Losses densities in the endplate, W/m3

- Hysteresis

- Eddy vector

- Eddy losses volumetric

## Comparison to Measurements (JINR / Dubna)

- Calculated 45.1 W    -        measured  42 +/- 2 W
- Good agreement with measurement results!

##  8 cases of dipole model

- •_Deep saturation_
- •Bmax=2 T, high coils, Endplate and brackets- from low carbon steel
- •Bmax=2 T, high coils, Endplate and brackets- from stainless steel
- •Bmax=2 T, low coils, Endplate and brackets- from low carbon steel
- •Bmax=2 T, low coils, Endplate and brackets- from stainless steel
- •_Low Saturation_
- •Bmax=1.5 T, high coils, Endplate and brackets- from low carbon steel
- •Bmax=1.5 T, high coils, Endplate and brackets- from stainless steel
- •Bmax=1.5 T, low coils, Endplate and brackets- from low carbon steel
- •Bmax=1.5 T, low coils, Endplate and brackets- from stainless steel

## Summary of 8 cases

- Eddy current and hysteresis losses for 8 cases are summarized in tables below
- Deep saturation 2 T          4 T/s
- Middle field 1.5 T             3 T/s

## Table of results for time averaged eddy (P) and hysteresis (Q) losses in Nuclotron dipole parts for single standard cycle (4 T/s) with no initial conditions, W

|  | HIGH COILS
FOR YOKE μr(Z)=25,
ENDPLATE AND BRACKETS ARE FROM STEEL 3 | HIGH COILS
FOR YOKE μr(Z)=25,
ENDPLATE AND BRACKETS ARE FROM STAINLESS STEEL | LOW COILS
FOR YOKE μr(Z)=35,
ENDPLATE AND BRACKETS ARE FROM STEEL 3 | LOW COILS
FOR YOKE μr(Z)=35,
ENDPLATE AND BRACKETS ARE FROM STAINLESS STEEL |
| --- | --- | --- | --- | --- |
| YOKE
(LAMINATED STEEL 3414) | 9.51 (P)
9.04 (Q) | 10.00 (P)
9.77 (Q) | 3.97 (P)
8.79 (Q) | 4.81 (P)
9.56 (Q) |
| ENDPLATE | 11.56 (P)
2.21 (Q) | 0.74 (P)
0 (Q) | 7.47 (P)
2.02 (Q) | 0.28 (P)
0 (Q) |
| BRACKETS | 14.46 (P)
5.42 (Q) | 2.34 (P)
0 (Q) | 14.54 (P)
4.84 (Q) | 1.53 (P)
0 (Q) |
| APERTURE TUBE
(STAINLESS STEEL) | 12.67 (P)
0 (Q) | 12.18 (P)
0 (Q) | 12.80 (P)
0 (Q) | 12.31 (P)
0 (Q) |
| YOKE, ENDPLATE, BRACKETS, APERTURE TUBE (SUM) | 48.19 (P)
16.67 (Q) | 25.25 (P)
9.77 (Q) | 38.77 (P)
15.65 (Q) | 18.93 (P)
9.56 (Q) |

## Table of results for time averaged eddy (P) and hysteresis (Q) losses in Nuclotron 

**dipole parts for single main operating cycle (3 T/s) with no initial conditions, W**

|  | HIGH COILS
FOR YOKE μr(Z)=35,
ENDPLATE AND BRACKETS ARE FROM STEEL 3 | HIGH COILS
FOR YOKE μr(Z)=35,
ENDPLATE AND BRACKETS ARE FROM STAINLESS STEEL | LOW COILS
FOR YOKE μr(Z)=45,
ENDPLATE AND BRACKETS ARE FROM STEEL 3 | LOW COILS
FOR YOKE μr(Z)=45,
ENDPLATE AND BRACKETS ARE FROM STAINLESS STEEL |
| --- | --- | --- | --- | --- |
| YOKE
(LAMINATED STEEL 3414) | 3.96 (P)
4.66 (Q) | 5.86 (P)
5.01 (Q) | 1.41 (P)
4.47 (Q) | 2.58 (P)
4.81 (Q) |
| ENDPLATE | 7.36 (P)
1.73 (Q) | 0.48 (P)
0 (Q) | 4.10 (P)
1.30 (Q) | 0.17 (P)
0 (Q) |
| BRACKETS | 1.91 (P)
1.10 (Q) | 1.15 (P)
0 (Q) | 1.00 (P)
0.64 (Q) | 0.47 (P)
0 (Q) |
| APERTURE TUBE
(STAINLESS STEEL) | 7.77 (P)
0 (Q) | 7.60 (P)
0 (Q) | 7.80 (P)
0 (Q) | 7.64 (P)
0 (Q) |
| YOKE, ENDPLATE, BRACKETS, APERTURE TUBE (SUM) | 21.01 (P)
7.49 (Q) | 15.08 (P)
5.01 (Q) | 14.31 (P)
6.41 (Q) | 10.87 (P)
4.81 (Q) |

## AC loss reduction - R&D phase: FEM calculations

**AC loss reduction - R&D phase:**** ****FEM calculations**

**Loss density in the end plate:**
**Replace by nonmagnetic, high el. resitive material**

**Eddy currents**

## AC loss reduction - R&D phase: FEM calculations

**Vectors of eddy current density in yoke at triangular current cycle**

**Hysteresis loss in the yoke**

**AC loss reduction - R&D phase:**** ****FEM calculations**

## AC loss reduction - R&D phase: Yoke restraint

**Vectors of eddy current density in brackets  at triangular current cycle**

- Hysteresis loss in the brackets

**AC loss reduction - R&D phase:**** ****Yoke restraint**

## AC loss reduction - R&D phase: Test models

- 1▲ partly _removed brackets_ and end plates
- 2▲ and laser cut _lamination slits_

**0.1mm laser cut**

**AC loss reduction - R&D phase:**** Test models**

- 3▲ _stainless steel_ brackets      and end plates
- 4▲ _reduced coil_ end shape

**1**

**1**

**2**

**4**

**3**

## R & D Results: AC loss reduction @ 4 K

- 	1. removed brackets (of made from SS)
- 	2. laser cut lamination slits
- 	3. minimized coil ends

**R & D Results****: ****AC loss reduction @ 4 K**

## SIS 100 Dipole: Beam pipe & cryopump 

- simulation of the eddy current loss density in the beam pipe

**SIS 100 Dipole: ****Beam pipe & cryopump**** **

## SIS 100 Dipole: Beam pipe & cryopump 

**SIS 100 Dipole: ****Beam pipe & cryopump**** **

**Schematic drawing of cross section of dipole vacuum chamber**

-  elliptical cross section
-  wall thickness: 0.3 mm (minimize AC-losses!)
-  strengthening of chamber by ribs
- Tmax < 15 K  (to be cooled by forced flow or 	         yoke)

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Section of quadrupole with SMP insertions in yoke

## ANSYS model of quadrupole with “high” coils

## Mesh for the quadrupole

## Example for comparison with measured value

** **Nuclotron Magnet
-  Standard Nuclotron coil
-  endplates and brackets from low carbon steel
-  standard current impulse
-  laminated yoke
-  packing factor 0.97 - 0.98
-  μr(Z) = 40

## Eddy current losses versus time

**Eddy current losses versus time**

- Yoke (average  3.5 W)

-  whole assembly  (average 18 W)

## Eddy current density in the yoke vs time, A/m2

## Vectors of the Lorentz force vs Time, N

## Average hysteresis losses density in yoke , W/m3

## Vectors of eddy current density in endplate vs. time 

- A / m2

## Hysteresis losses in endplates

## Eddy losses in the brackets vs time

## Eddy losses density in brackets vs time 

- W / m3

- Eddy losses density in brackets vs time

## Hysteresis Losses in the brackets

**Nuclotron Quadrupole :**

- Nominal gradient: 34 T/m
- Ramp rate: 68 T/(ms)

**R & D Results: ****loss reduction in quadrupoles**

**▲****Test measurements  on quadrupol modifications **
**◄ ****FEM calculations on detailed 3D-models**

## R & D Results: loss reduction in quadrupoles

- MODEL QUADRUPOLE AT THE LHE JINR TEST BENCH** **

**R & D Results: ****loss reduction in quadrupoles**

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation
- Validating AC Loss calculation
- Results
- In Detail Models
- Dipole / Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
-  Field quality calculation
- Outlook
- Conclusion

## Relaxation: Simplified laminated yoke- second approach: 4 cycles without pauses

- fp = 1   z = z (H)

- fp = 0.94-0.98    z =25

-  ideal packing factor
-  loss only during ramp up
-  not much change from 3 to 4 pulse
- long relaxation time

-  realistic packing factor
-  loss during ramp down a bit smaller
-  faster relaxation
-  after two pulses nearly stable

## Relaxation: Detailed Model –yoke assembly   1, 5 and 10 Hz                  I/II

## Relaxation: Detailed Model            II/II

- Loss per cycle.
- Squares ... hysteresis
- Circles ... eddy currents
- Triangles ... hysteresis + eddy currents

- Losses per cycle
-  non linear dependence on     frequency
-  common approach of ***linear fit*** to measurement for  hystersis and eddy current losses ***Not valid***!

## Contents

- SIS 100 Magnets
- Magnet modeling
- Motivation  Requirements
- Implementation /  Validation
- Results
- In Detail Models
- Dipole
- Quadrupole
- Relaxation in Dipoles
- Full scale prototype designs
- Dipole
- Quadrupole
- Outlook
- Conclusion

## Transient process in single plate in Bxy field:

- the transient processes in single plates of magnets from Bxy field have to been calculated for:
- effect of the Bxy field at low temperature for fast cycling magnets
- possible for boosters and compact medical synchrotrons

**thickness 0.5, 1 and  5 mm, **
**frequencies of triangle cycles: 1 and 10 Hz**

## Geometry of the yokes single laminate

## Time dependencies of eddy current power from Bxy

- Upper - 1Hz, lower -10 Hz  (0.5 mm - 1 mm - 5 mm with rho=0.31x10**-6 Ohmxm at 4.2 K (LC steel  has 0.08-0.12x10**-6 Ohmxm and higher AC losses!)

## Vectors of eddy current density from BXY in single laminate (0.5 mm) per time (f = 1 Hz), A/m2

## Eddy losses density from BXY in single laminate (5 mm) per time (f = 1 Hz), W/m3  Compare with above case of Bz source

## 2D geometry for static and dynamic calculations of the averaged BX in bracket

***Averaged induction B******X******  for static and transient solution***

## Eddy current loss in the brackets (similar to 3D case!)

***Eddy current loss in the brackets****** ******(similar to 3D case!)***

***Eddy currents in 2D brackets (t = 0.48 s)***

***B******X****** along path in static and dynamic***

## Prototype Dipole (3 meter long): Features

-  2D
-  slits for field quality improvements
-  laminated yoke
-  3D
-   slits in the ends
-  brackets with holes
-  bulk end plates
-  Rogowsky end pole shape
-  elliptical beam pipe
-  support structure
-  cooling tubes
-  All in one model
-  careful meshing for acceptable calculation time

## Mesh of the yoke

## Meshes : Radial Harmonics

**RADIAL “FAN” MESH FOR ACCURATE HARMONIC COEFFICIENTS CALCULATION**

## Fourier Field Coefficients

-  field homogeneity in aperture specified  < 500 ppm
-  calculation error well below
-  different meshes
-  tested:
-        Br harmonics= Btheta harmonics in central cross section
-  unallowed harmonics = 0
-   skew harmonics = 0
-  2D / 3D calculations comparison
-  same for central field of long magnet
-  in the aperture based on triangular prism

## Static and dynamic field in the beam aperture  

- Static and dynamic field in the beam aperture**  **

- Circles for field coefficients calculation

## Field Aspects of the Dipoles

**|B|**  0.1 T  – 2.6 T
- highest field  in aperture  near  to the  end due to end field loop
- verified by measurement for SIS 18 magnets (conventional ones)

**B****z**  -1.5 T  – 2.4 T
- Source of AC losses near the magnet end

## By in aperture

- By in aperture

- homogeneity
- d By / By
- - 10-3 – 10-3

- By  2.195 T – 2.24  T

## Static and dynamic field in the beam aperture : Short dipole end plates and Brackets – LC steel 

- Eddy current effect
- 1 unit = 100 ppm

## Static and dynamic fields in full scale prototype dipole and quadrupole: cross section and integrated

- Precise mesh allow to calculate the static central and integrated harmonic coefficients and dynamical impacts from yoke assembly and stainless steel beam pipe
***Mesh for integrated coefficients determination***

## Conclusion                                                 I /II

-  parameterized models
-  can calculate :
-  field in the aperture and the yoke
-  eddy currents
-  hysteresis losses
-  R & D steps
-  simplified model  for dipole
-  results within good agreement with experiments
-  computable in acceptable time

## Conclusion                                                 II/II

-  matched measurements
-  loss per cycle *does not* depend linearly on the frequency
-  studied different options
-  brackets with holes from low carbon steel, stainless steel
-  end plates: low carbon steel / stainless steel
-  full scale prototype
-  able to predict losses
-  calculate (integral) 3D field multipoles

## Analysis of:
Nuclotron cable design 
Insulation concept
winding scheme
technological optimization
ANSYS Models
Substrate: comb or block
model coils production
mechanical tests 

**Nuclotron cable design **
**Insulation concept**
**winding scheme**
**technological optimization**
**ANSYS Models**
**Substrate: comb or block**
**model coils production**
**mechanical tests**

- Outlook: **technological and FEM investigations**

**cable ****▲**
**2D coil ****►**
**3D coil end ****▼**

## Outlook: Coil R&D for insulation technique

- Outlook: **Coil R&D for insulation technique**

**All-Kapton**
-  On top of two layers of normal Polyimide, two additional layers of adhesive Polyimide are wound

**SC cables with Prepreg insulation and comb elements**

## Outlook: Increase coil mechanical stability 

- Outlook: **Increase coil mechanical stability **

-  **comb structure elements (G11)**

## Outlook: Models for coil mechanical design 

-  New winding scheme for technological improved layer transition !

**for:**
-  reduction of  point loads
-  accurate positioning

## Outlook

-  Coupling analysis
-  Magneto – Thermal
-  Magneto – Mechanical (Lorentz forces)
- AC losses in superconducting coil
-  (and field affects due to SC current carriing element)
-  Hysteresis in SC filaments
-  Matrix in composite wire
-  Cable loss due to inter strand contact
- ALL needed for pulsed magnet design calculations
-  Curved Magnets
-  Full Magnet System at 1- 10 Hz repetiton rate (mesh is ready now)