Superconducting Magnet Conceptual Design

Riccardo Musenich

April 9th, 2014

Several approaches to magnetic shielding were

proposed:

Large single turn

Solenoids

Toroids

Magnetic lens

Magnetic Shielding

zHabitable Module

r

Solenoidal Shield

Br

Toroidal shield

ei RRRR

NIB <<=

20

πµ

Ideal toroid

Habitable

ModuleBr

Shielding Power of a Toroidal Magnet

i

eR

R R

RNIBdR

e

i

ln∫ ==Ξπ

µ20

Re

Ri

For an ideal toroid, the shielding power is defined as

Shielding Power of a Toroidal Magnet

Ξ=

i

e

R

R

lE

ln0

2

µ

π

−

Ξ−=ie

i

eRR

R

R

lF

11 2

0

2

lnµ

π

Quantities like the stored energy and the inward force

can be written as a function of the shielding power

It allows computing the maximum energy of the

shielded particles:

( )

+

−Ξ−−= 1

1

1

2

0

20

ϕη sincm

qcmEK

Toroidal Shield

Real toroid

Racetrack coils Tilted solenoids

(double helix)

Toroidal Shield

12

21

Toroidal Shield

1

2

21

0 2 4 6 8 10

R [m]

0 2 4 6 8 10

R [m]

Real toroidal magnets

Ripple

(period: 2π/n)

Increasing the number of coils, the amplitude of

azimuthal field oscillation decreases.

The effect of the ripple on the shielding power

is negligible if the n≥12:

( ) 010112 . minmax ≤ΞΞ−→≥n

Real toroidal magnets

To minimize both the fringe field and the

maximum field at the conductor, the magnet

must tend to an ideal toroid:

• Increasing the number of coils

• Increasing the winding aspect

ratio w/d

Shielding

Ξ = 5 Tm

Shielding

Due to the peculiar application a new kind of

conductor is proposed for the SR2S magnet

Conductor

Conductor

MgB2 conductor with welded copper strips.

www.columbussuperconductors.com

Titanium clad MgB2 conductor + aluminum strip

Cross section area = 10 mm2 (15% MgB2, 40% Ti, 45% Al)

Average mass density: 3400 Kg/m3

Operation temperature: 10-15 K

Why MgB2 ?

High stability

No helium cryogenics

Low density (~1/2 respect to YBCO CC)

Conductor

Stability:

Respect to NbTi conductors operating at 1.8 K, a MgB2

conductor operating at 10 K is more stable.

If the temperature margin is 1 K :

AMS conductor (Al stabilized Cu/NbTi)→ ΔH=420 J/m3

SR2S conductor (Al stabilized Ti/MgB2)→ ΔH=2000 J/m3

Conductor

• Winding: pancake coils

• Operative current density: Je=70 A/mm2

the operative current density is referred to the whole

conductor cross section. It is limited in order to protect the

magnet in case of quench.

• Current: I=700 A

• Total current: 46.2 106 A-turns

• Maximum field at the conductor : B=4 T

Magnet

The magnet dimensions are limited by the next heavy launchers

4 launches → Rext=6.3 m 6 launches → Rext=9.5 m

1 launch of a whole magnet → Rext=4.5 m

Launch

MAGNET MAIN PARAMETERS

Current Density

Current per cable

# of turns (per racetrack) 55

# of layers (per racetrack) 10

# of Racetracks 120

Bending Power 7.51 Tm

Bmax over conductor 3.7 T

Stored Energy 953 MJ

Inductance 3890 H

Magnetic Parameters

The magnet will operate in persistent mode

Superconducting joints between MgB2 cables already developed

Magnet sectors assembled in orbit → resisNve joints

High inductance

negligible

Decay time: 45 years

2 year mission → ΔΞ/Ξ< 0.05

Magnetic Field Stability

01

=+++

∑ nc

n

cj j I

IRIR

dt

dIL

nn

cII 1+

Inward forces

Intra-coil forces

Forces and torques

−

Ξ−=ie

i

eRR

R

R

lF

11 2

0

2

lnµ

π

Any asymmetry due to mis-positioning or non

uniform current distribution (short in case of

quench) generates forces and torques on the

coils

Forces and torques

Forces and torques

FORCES AND TORQUES PER RACETRACKS

Radial Forces on the inner bar -3.36 MN

Radial Forces on the outer bar 1.56 MN

Difference acting on the inner

cylinder

-1.80 MN

Axial Force on the outer arc 0.20 MN

Axial Force on the inner arc 0.36 MN

Axial Force on the arcs bar 0.88 MN

MAX Torque if one racetrack is

off

6.94 MNm

* referred to 120 coils , “4 launches” configuration

*

Internal structure to hold the inward forces

Mechanical Structure

Hypothesis of mechanical structure

Tie rods to hold the coil internal forces

A structure connecting the coils is required to support torques

The magnet system is weakly connected to the habitat. The tie rods have to

support only the forces due to the spacecraft acceleration.

The use of advanced materials will be studied:

Cermets (Al - Boron carbide)

Carbon fibers (tensile strength up to 1000 GPa)

Aramid fibers

Foams

Mechanical Structure: What Next?

Deep space offers favourable conditions to cryogenics

(low temperature and low pressure)

Then main heat load comes from the habitat through radiation

Absence of gravity and weak accelerations → low heat conduction

Cryocoolers can provide the required power

Solid hydrogen could be used as enthalpy reservoir

Due to the large magnet dimension, heat connections are the

most important components to be developed

Cryogenics

Quench

Comparison between the ATLAS and the SR2S barrel toroids

ATLAS SR2S

Stored energy [MJ] 1000 950

Inductance [H] 5.12 3890

Je [A/mm2] 30 70

JAl [A/mm2] 32 233

I [A] 20500 700

Conductor mass [tons] 100 36.3

E/m [kJ/kg] 10 26

Active quench protection is required

Coil subdivision can be a possible option to

improve the protection

Quench

The SR2S magnet is a modular superconducting

toroidal system based on a cutting edge conductor.

Due to the new conductor, the ligth mechanical

structure and the high energy density, the SR2S

magnet is well beyond the state of the art.

Its peculiar application demands for advanced

materials and for innovative solutions in the field of

magnet technology.

Conclusions

THE END

Slide di riserva

Magnetic flux density of an ideal toroid:

Bending power:

Lorentz forces acting on the particle:

Slide di riserva

In order to know if a particle is deflected inside the magnet, we need to find the

minimum of the trajectory along r, i.e. the radius rm corresponding to the particle

maximum penetration, imposing

In the particular case of a particle

moving on a z-r plan:

( )( ) 22 vrvmtm

≤− ϑϑ&

&

( )( ) mm

e

m

e

m rrr

r

r

r≥→≤ ϑ

ϑ&

&

lnln

Slide di riserva

Particles moving on a z-r plan are the most penetrating

Analytical solution ( ) for rm and bending power Ξ:

The bending power can be written as a function of the properties of

the incoming particle:

Cut-off energy:

( )ϕγ sin−−=Ξ 1120 cq

m

( )

+

−Ξ−−= 1

1

1

2

0

20

ϕη sincm

qcmK