**Transverse magnetoresistance** of Cu and Al at cryogenic temperatures:

lss.fnal.gov- Strong field hampers much the high conductivity obtained by cold.
- Aluminium is abnormally insensitive to the field.
- The cyclotron coil remains valid, the 30T electromagnet is much affected.

In the more favourable transverse effect, the induction is perpendicular to the current. It happens at electromagnets like here.

========== Cyclotron coil

For 2t in the gap, each coil provides 176kA that create up to 0.7T or 7kOe in the 0.3m wide slit hosting the coil. From fig.1 in the pdf, the magnetoresistance would add 1.4× the zero-field resistivity of Al.

The 0.7T appear only near the open end of the slit, so the 1.4× is reduced by /3 as a mean, or rather by /2 as the current redistributes.

The pillars carrying the return flux cover only half of 360°. Where they're absent, the induction is around /3 and the 1.4× drops even more. Almost a factor /2 gained over 360°.

The pillars can stand farther away to reduce the induction through the coils. Improve easily /2. They can also be thicker and narrower to improve the gain over 360°.

So the

**magnetoresistance adds rather 0.35× at the sketched cyclotron coil, and with minimal optimization 0.1×**. Fine.

========== 30T electromagnet

The field reaches 30T or 300kOe at the coil's inner face and almost as much at the outer face.

Fig.2 shows Cu up to 100kOe, so if Kohler's law holds, the magnetoresistance adds up to 170× to the cold resistivity, ouch.

Fig.1 shows Al measured up to 40kOe: if daring to extrapolate linearly the curve of 2100 residual resistivity ratio (RRR) to 300kOe, the magnetoresistance adds up to 6.2× to the cold resistivity, provided that the current distribution is stable.

The field increases linearly from zero at the section's centre point but decreases beyond a half-thickness, so we can count 2/3 of the 6.2×, that is 4.1×.

Purer Al can rescue the chiller consumption. Increasing the RRR from 2100 to 28200 worsens by 2.8 the magnetoresistance but it's relative to the zero-field cold resistivity which drops by 4 to 5, providing a net 1.6 gain.

Together, magnetoresistance makes the ohmic loss and chiller power 3.6× worse than I estimated in the previous message:

**1.9MW instead of 10MW lukewarm**. Still interesting. Reooptimize the temperature?

========== Laminar flow

I supposed a laminar helium flow, but η=35µP=3.5µPa×s doesn't help the intuition. ν=η/ρ=1.4mm

^{2}/s and 13mm/s in 100µm channel width define Reynolds Re=u×h/ν ~1 <<2000 so the flow is laminar.

Marc Schaefer, aka Enthalpy