Cryogenic Systems

CuNi Cable

Q: Why is CuNi coax used in dilution refrigerators instead of copper coax?

Copper-nickel (typically 70/30 Cu/Ni) has a thermal conductivity near 23 W/m-K at room temperature and only about 1 to 2 W/m-K below 4 K, roughly two orders of magnitude lower than oxygen-free copper at the same temperature. In a dilution refrigerator the cold stages have cooling powers measured in microwatts to a few hundred microwatts, so a single copper coax could conduct enough heat to overwhelm the mixing chamber. A semi-rigid CuNi line conducts only tens of microwatts across a stage span, letting a system route dozens of signal lines to the millikelvin plate. The price is higher RF loss, since CuNi has roughly 30 times the electrical resistivity of copper, so attenuation is managed by frequency-dependent stage placement and added cryogenic attenuators.

Q: How much heat does a CuNi coax conduct between fridge stages?

Conducted heat follows Fourier's law integrated over temperature, Q = (A/L) times the integral of k(T) dT between the two stage temperatures. For a UT-085 size CuNi line (outer diameter 2.2 mm, length about 0.2 m) running between the 4 K and 1 K stages, the cross section and the low integrated thermal conductivity yield a heat leak on the order of 10 to 50 microwatts per cable, dominated by the outer conductor. Engineers use published conductivity integrals for CuNi to budget the total line count against the available cooling power at each plate, and they thermally anchor (heat sink) every line at each stage so the conducted load is intercepted by the higher-power stages above.

Q: What is the RF insertion loss of CuNi coax at microwave frequencies?

Attenuation scales with the square root of frequency because of the skin effect, and CuNi's high resistivity makes the loss far higher than copper or silver-plated lines. A semi-rigid 2.2 mm (UT-085) CuNi cable shows roughly 5 to 8 dB/m at 5 GHz and 12 to 18 dB/m at 20 GHz at room temperature, with loss dropping modestly as the cable cools and resistivity falls. For drive and readout lines this loss is often a feature, since signal attenuation also attenuates room-temperature thermal noise traveling toward the qubit. For sensitive output lines, designers instead use superconducting NbTi coax above the HEMT amplifier to avoid the loss penalty while keeping heat leak low.

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Coaxial cable built from a copper-nickel alloy (commonly 70/30 Cu/Ni) used to carry RF signals between the temperature stages of a cryostat or dilution refrigerator. Its low thermal conductivity, roughly two orders of magnitude below oxygen-free copper near 4 K, sharply limits the heat conducted down each signal line, which is the dominant constraint when a cold stage offers only microwatts of cooling power. The trade is high RF insertion loss: CuNi resistivity is about 30 times that of copper, so a UT-085 line runs near 5 to 8 dB/m at 5 GHz. On qubit drive lines that loss is welcome because it also attenuates room-temperature thermal noise, making CuNi a standard choice for the upper drive and readout segments of quantum and cryogenic measurement systems.

Alloy: 70/30 Cu/Ni

k at 4 K: ≈ 1 to 2 W/m·K

Loss (UT-085, 5 GHz): ≈ 5 to 8 dB/m

Balancing Heat Leak Against RF Loss in Cryogenic Wiring

The wiring problem inside a millikelvin cryostat is fundamentally a conflict between two transport mechanisms in the same metal. Electrical conduction and thermal conduction both favor a high-purity metal like copper, but a cold stage with only a few hundred microwatts of cooling power cannot tolerate the heat that a copper coax would drag down from warmer plates. Copper-nickel alloy breaks the tie. Adding roughly 30 percent nickel scatters both electrons and phonons, raising electrical resistivity to near 49 micro-ohm-cm and collapsing the low-temperature thermal conductivity, while leaving the cable mechanically robust and easy to solder and form as a semi-rigid line.

In practice the outer conductor dominates the conducted heat because it carries most of the cross-sectional metal, so engineers select a cable diameter (UT-034, UT-047, UT-085, UT-141) to set the heat-leak budget per line. Every line is also heat-sunk, or thermally anchored, at each stage so that the load conducted from above is intercepted by the higher-cooling-power plates rather than reaching the mixing chamber. Because attenuation rises with the square root of frequency through the skin effect, the same CuNi loss that hurts a sensitive output line is deliberately exploited on input lines to suppress thermal photons descending from the 300 K electronics.

The result is a layered wiring scheme. Input and drive lines often use lossy CuNi (or beryllium-copper) on the upper stages, while delicate output lines switch to superconducting NbTi coax above the first cryogenic coaxial cable amplifier stage, where preserving signal energy matters more than adding loss. CuNi therefore occupies a specific niche: the segments where you want both low heat leak and intentional attenuation.

Governing Relations: Heat Leak and Skin-Effect Loss

Conducted Heat (Fourier integral form):
Q = (A / L) × ∫_{T_cold}^T_hot k(T) dT [W]

Skin-Effect Attenuation:
α ≈ (R_s / 2Z₀) × (1/a + 1/b), R_s = √(πfμρ)

Thermal-Noise Suppression by Attenuation A (dB):
T_added ≈ T_warm × 10^(−A/10) [K, photon equivalent]

Where A = conductor cross-section, L = stage span, k(T) = temperature-dependent thermal conductivity, R_s = surface resistance, ρ = resistivity (≈ 49 μΩ·cm for 70/30 CuNi), a/b = inner/outer conductor radii, Z₀ = 50 Ω. Example: 20 dB of CuNi attenuation cuts a 300 K noise contribution to about 3 K.

Cryogenic Coax Material Comparison

Conductor Material	Resistivity (μΩ·cm)	k near 4 K (W/m·K)	RF Loss	Typical Use
CuNi (70/30)	≈ 49	≈ 1 to 2	High	Drive / input lines, attenuating segments
Beryllium-Copper (BeCu)	≈ 7	≈ 5 to 10	Moderate	Intermediate-stage lines, springy contacts
Stainless Steel (304)	≈ 70	≈ 0.3	Very high	Lowest heat leak, very lossy lines
NbTi (superconducting)	0 (below T_c)	≈ 0.1 to 0.5	Very low	Output / readout lines above HEMT
OFHC Copper	≈ 0.2 (low T)	≈ 300 to 2000 (RRR)	Very low	4 K thermalization, high heat leak

Common Questions

Frequently Asked Questions

Why is CuNi coax used in dilution refrigerators instead of copper coax?

CuNi (70/30) thermal conductivity is near 23 W/m·K at room temperature and only about 1 to 2 W/m·K below 4 K, roughly two orders of magnitude under oxygen-free copper. Cold stages supply only microwatts to a few hundred microwatts of cooling power, so a copper coax could overwhelm the mixing chamber. A semi-rigid CuNi line conducts only tens of microwatts per stage span, letting a system route dozens of lines to the millikelvin plate. The price is roughly 30× the resistivity of copper, so RF loss is managed by stage placement and cryogenic attenuators.

How much heat does a CuNi coax conduct between fridge stages?

Heat leak follows Q = (A/L) × ∫ k(T) dT between the two stage temperatures. For a UT-085 line (2.2 mm OD, ≈ 0.2 m) between the 4 K and 1 K stages, the low integrated conductivity yields about 10 to 50 μW per cable, dominated by the outer conductor. Engineers budget the total line count against each plate's cooling power using published CuNi conductivity integrals, and heat-sink every line at each stage so the load is intercepted above.

What is the RF insertion loss of CuNi coax at microwave frequencies?

Attenuation scales with √f from the skin effect, and CuNi's high resistivity makes it far lossier than copper or silver-plated lines. A semi-rigid 2.2 mm (UT-085) CuNi cable runs roughly 5 to 8 dB/m at 5 GHz and 12 to 18 dB/m at 20 GHz at room temperature, easing slightly as it cools. On drive lines that loss is a feature, since it also attenuates descending thermal noise. Sensitive output lines instead use superconducting NbTi above the HEMT stage to avoid the loss.

Related Terms

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