A compact, low-power <1K cooling platform for
superconducting nanowire detectors
Emily Ronson, Simon Chase and Lee Kenny
Chase Research Cryogenics, Cool Works, Unit 2 Neepsend Ind Est, Parkwood Road,
Sheffield S3 8AG, United Kingdom;
Abstract. Superconducting nanowire single photon detectors (SNSPD) with high detection
efficiency, low dark count rate, small timing jitter and short recovery times require cryogenic
cooling. Detector performance is strongly dependent on temperature and though many detectors
will operate at ~4K, lower temperatures offer significant performance gains. Fortunately , the
technology for sub-Kelvin cooling is now mature and products are available that offer simple
operation, with reliable and repeatable performance at relatively low cost. In this paper we
review performance data from tests on more than 45 individual sub-Kelvin modules
manufactured by Chase Research Cryogenics. We compare modules of different sizes and
discuss how modules can be scaled to achieve a range of technical specifications for specialised
In the last few years, Chase Research Cryogenics has designed and built many closed-cycle 4He modules
for customers with a wide range of user applications. These modules vary in size, weight, power
consumption, heat lift capacity, base temperature and run time. In this paper three differently-sized 4He
modules are discussed, the 4 STP litre modules are designed for a run time of approximately 10-12 hours
under a 100μW load, the 10-12 STP litre modules are designed for a run time in excess of 20 hours
under a 100μW load, and the 33 STP litre modules are designed to run for more than 12 hours with a
1000μW load . All three module sizes are designed to run at a temperature below 1K.
The run time is determined primarily by the total quantity of 4He in the module. After
condensation to liquid, the 4He is evaporated by the combined load from the user’s apparatus (e.g.
SNSPD array) being cooled by the module, and by base load. The base load encompasses all
mechanisms for evaporating 4He that are not directly due to the user’s apparatus. These mechanisms
include, but are not limited to, heat conduction up the pumping tubes, superfluid film creep and radiative
loading on the head of the module. Their contribution to base load is determined by the design
parameters of the module, which we discuss in this paper. A simple mathematical model of the helium
condensation process, as described by Pobell , has been used to estimate the cooling power and base
load for each module size.
A wide range of SNSPD devices require cryogenic cooling, though they do not necessarily
impose high cooling power requirements . Sub-Kelvin 4He modules with a short initial cool down
and time long run time may be optimal for many low-temperature detector applications, and we discuss
the best way to achieve this specification.
The 4He modules described in this paper are compact sealed units that are simple to operate. They consist
of a cold head (where the temperature reaches below 1K); a film burner, which contains an orifice to
control super fluid film creep; a main plate; and a cryopump that contains activated charcoal. A gas gap
heat switch is connected between the cryopump and the main plate. The main plate is pre-cooled via a
thermal link to either a liquid 4He (L4He)-cooled plate or a ‘dry’ mechanical pre-cooler (e.g. a Gifford-
McMahon or Pulse tube).
The operation of 4He modules is well described in the literature [3,4]. Basic procedure entails
pre-cooling the module’s main plate and head to below 4.2K. The cryopump is then heated in order to
drive the 4He gas off the charcoal and condense it into the head, which is mounted lowermost during
operation. Once all the 4He has condensed, the pump heater is turned off and the gas gap heat switch is
turned on to cool the pump to the temperature of the main plate. This allows the gas to be adsorbed into
the pump once again and the liquified 4He in the head continues to cool until its vapour pressure is in
equilibrium with the internal pressure of the module. At this point the module is running at its base
temperature. The module will keep running until the liquid 4He in the head is exhausted, when it can be
recycled by reheating the pump. Recycling takes approximately 1 hour. The temperature of the head
while running will depend on design parameters and applied loads.
3. Methods and Material
Tests have been carried out to verify the performance of more than 45 4He modules manufactured over
the past ~5 years. These modules are in three very different sizes, containing 4, 10-12 and 33 STP litres
of 4He gas. The 4-litre module has the shortest tubes connecting the head to the pump. The 10-12 litre
and 33 litre modules are of similar design with off-centre pumps and longer pump tubes, but differing
size pumps and heads. Across all three modules, the size of the superfluid containing orifice, and the
diameter of the pump tubes, both increase with module size. Dimensional parameters can be found in
Table 1, and images of CAD models in Figure 1.
Figure 1. CAD models of 4, 10-12 and 33 litre modules (different scales).
Each test was carried out in a L4He-cooled cryostat. Temperature measurements were made
using a ruthenium oxide temperature sensor on the module’s head, a diode or ruthenium oxide
temperature sensor on the film burner, a diode on the pump and a diode on the switch. Resistive heaters
on the pump and the heat switch were used to control the module’s operation. A resistive load heater
was also mounted on the head of each module, for testing the response to loading by varying the voltage.
Data were collected using either Lakeshore Cryotronics or custom-made thermometry equipment, with
software control via a Labview VI.
Table 1. Dimensional Parameters.
Module Height (mm)
Main plate diameter (mm)
Each module was tested against the customer’s specific requirements, so each test sequence
varied slightly. When possible, load response data were acquired by applying a load to the head and
waiting for the temperature to stabilise, then repeating this process over a specified range of loads. Once
the load response test was complete the module was run under a customer-specified load to expiry,
which enabled us to verify that the module met the run-time specification. The run time was calculated
as the total length of time the module head spent at a temperature below 1K. The typical loading
specification for 4 litre and 10-12 litre modules was 100μW and for 33 litres was 1000μW. When
possible, a second run was completed with no applied loads in order to estimate the base load on the
Our mathematical model was used to estimate the condensation efficiency, for each module
size, from the total number of moles of 4He in the module, the internal volume, and the temperatures of
both the head and the pump during condensation. The temperature values used in the model were
averages of the measured values for each size module. The cooldown to base temperature was also
modelled to calculate the total cooling power available to the module at the start of the run. The base
load was then estimated from the total run time when there was no applied load, i.e assuming the
condensed helium charge was consumed solely by the base load.
4.1 Experimental data
Table 2 shows the average head temperatures for some standard loading conditions on the modules. The
4 litre and 10-12 litre modules were all tested with both no load and 100μW load, and the 33 litre
modules were tested using a higher loading condition at 1000μW.
Table 2. Temperature comparisons.
Table 1. Run time comparisons.
Run time (hours)
Table 3 shows the run time of modules under different loading conditions, in each case the module
was run to expiry under the stated load. Note that the largest module was designed to run under
significantly higher loading conditions and at low temperatures.
Figure 2, Figure 3, and Figure 4 show the load response data for each module size. Figure 2 contains
data from 8 individual 4 litre modules, Figure 3 contains data for more than 30 individual 10-12 litre
modules, some of which were tested several times with different loading conditions, and Figure 4 shows
data for 7 individual 33 litre modules. In Figures 2 and 3, lines are fitted to the data using least squares,
whereas in Figure 4 the data are fitted with a power function. All three fitted relationships are compared
in Figure 5, which shows 95% confidence intervals for each relationship.
Figure 2. 4 litre module load response to loading.
Figure 3. 10-12 litre module response to loading.
0 50 100 150 200 250 300
Head load (μW)
0 50 100 150 200 250 300 350 400
Head load (μW)
Figure 4. 33 litre module response to loading.
Figure 5. Comparison of loading responses for different module sizes.
4.2 Modelled Results
Table 4 shows the estimated total cooling power and base load for each module size. Note that higher
cooling powers would be expected if the modules were pre-cooled using a mechanical pre-cooler, as the
condensation conditions are more favourable . These modules would run for significantly longer in a
liquid-cryogen-free system with a mechanical pre-cooler.
0 200 400 600 800 1000 1200 1400 1600 1800
Head Load (μW)
0 200 400 600 800 1000
Head Load (μW)
4L Load Response
10-12L load Response
33L Load Response
Table 4. Calculated cooling powers for each size module, with a L4He-
Cooling Power (J)
Base load (mW)
In Figure 6 we explore the relationship between the size of the orifice that controls superfluid
film creep and the observed performance of the modules. The orifice sizes are normalised in ratio to the
orifice of the 10-12 litre module; the 4 litre module has the smallest orifice and the 33 litre module the
largest orifice. A smaller orifice constrains the film creep more, which in turn reduces the base load.
However, a smaller orifice also results in a higher head temperature at a given load, and a steeper
response to applied loads.
Figure 6. Relationship between orifice size and various parameters.
The physical dimensions of the modules considered here are not scaled in direct proportion to the volume
of 4He in the module. This makes some comparisons between the different module sizes indicative rather
than quantitative. For example, the total cooling power of the module does scale in proportion to the
module’s 4He volume, but the base load, which determines the run time of the module, does not (Table
4). That is because the base load depends strongly on the orifice size and on other physical dimensions
that are not in scale with the 4He volume.
The 4-litre module has been designed as part of a continuous cooler, in which a pair of
modules, cycling in antiphase, alternately cool a cold head that stays below 1K indefinitely . Each
module needs a low load and short run time; as a minimum it must run for the length of time it takes to
recycle the other module. So, in principle this module could be made even smaller as the run time could
be much shorter than 12 hours. Alternately, the orifice size could be made larger to reduce the base
temperature, while sacrificing run time.
0.8 1 1.2 1.4 1.6
Slope of temperaute dependance
Average Base load (mW)
Ratio of orifice size
average base load mW slope of temperature dependance
For the 4 litre modules tested here, the orifice was manufactured using a different method to
the other modules, which resulted in greater variability between individual modules. The confidence
intervals in Figure 5 are larger than the other modules, and the standard deviations of the run time and
head temperature are larger in Table 2 and Table 3.
The 10-12 litre modules are a standard product; over 30 have been made and so their
performance is very well characterised. These modules are suited to low-load applications requiring
long run times. The 10-12 litre module can be configured to bolt directly onto a very small, low-powered
GM pre-cooler that uses a compact air-cooled compressor. When pre-cooled in this way their run time
is increased by approximately 25% .
The 33 litre modules are designed for higher loading applications. This module requires a
larger mechanical pre-cooler as the peak power consumption is high. The module is also too heavy to
bolt directly onto the mechanical pre-cooler, which makes the cryostat design more complex.
When considering the factors that contribute to the base load in the different modules, losses
due to heat conduction between head and pump are not thought to be a dominant component of the base
load . Most of the heat conduction occurs along the tubes between the head and the main plate as the
temperature gradient is greatest between these points whilst the module is running. The tube lengths and
wall thickness are similar in each module design, and for comparison between module sizes can be
considered effectively constant. The tubes between the pump and the main plate do vary in length and
size between the modules, but this will have only a small effect on heat conduction because when the
module is running, the heat switch is on, and the pump and main plate are very close in temperature.
The radiation load on the head is proportional to the surface area of the head, which increases
with module size. However, each module was tested in a L4He pre-cooled cryostat with similar
configuration and radiation shields at 4K and 77K, so external loading can be considered effectively
constant. Internal radiation loading due to the ‘hot’ pumps will differ as the larger pumps have a larger
thermal mass. The pump is located under the main plate opposite the head for each module, so direct
radiation to the head is limited. When the pump is hot and radiating onto the head, gas convection is
cooling the head, so the net effect of the radiation is very limited. While the module is running the pump
is cold and has very low thermal emission.
The flow of helium from the cold head to the cryopump can be split into two components,
superfluid film creep and gas flow. The orifice constrains the creep of superfluid helium, which is
independent of loading conditions but depends on the true circumference of the edge of the orifice. In
principle a ‘good’ orifice should have a knife edge so that its circumference is well-defined e.g. there is
minimal surface roughness at the edge . At low applied loads the quantity of helium leaving by
superfluid film creep is much greater than by gas flow. A smaller orifice restricts the superfluid creep
more and results in a lower base load, as shown in Figure 6. At higher applied loads a greater proportion
of helium leaves the head by gas flow, the rate of which will depend on the area of the orifice. When the
orifice is small and the load is large, the orifice also restricts the gas flow by trapping hot gas. This
causes a larger temperature rise in response to loading, as observed in Figure 5 for the 4 litre module.
The 33 litre module has a larger orifice that does not restrict the gas flow for high loads, but it produces
a larger superfluid film creep and results in a higher base load, reducing the overall run time.
Our results illustrate the trade-offs between different performance parameters, which must be
optimised for the specific application. For many SNSPD applications the loading conditions are minimal
and a small module offering quick cool down and warm up, allowing experiments to be run over short
periods of time, may be most useful. Commercial SNSPD products need a well characterised module
with reliable and repeatable performance, ideally that can recycle overnight or run continuously. Such
systems will seldom be opened or warmed up to room temperature. Both the 10-12 litre and 4 litre
modules offer simple operation with low power consumption, both can be mounted either directly to a
mechanical pre-cooler, or to an interface plate with thermal link to the pre-cooler.
In this paper we have shown that the characteristics of 4He sub-Kelvin modules are well understood and
it is possible to design modules that are optimised for specific applications. Increasing the volume of
helium in the module increases the total cooling power available, but larger modules require larger
mechanical pre-coolers and more complex cryostats. Increasing the size of the superfluid creep-
controlling orifice will increase the base load and decrease the run time, but also decrease the running
temperature and reduce the temperature response to loading. These characteristics must be traded off to
optimise the performance of the module for the application. For commercial applications, overall cost,
reliability, reproducibility, and simplicity of operation may be as important as overall performance.
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