CryoGS: Cryogenic Geometric Anti-Spring Filter

• CryoGS is a compact cryogenic geometric anti-spring isolation system designed to suppress low-frequency vibrations in closed-cycle cryostats.
• The device employs a monolithic radial blade GAS configuration that reaches a sub-200 mHz vertical resonance at 7 K, reducing problematic 1 Hz vibrations by an order of magnitude.
• It incorporates precise load and compression tuning via mechanical adjustments and in-situ voice-coil actuators to overcome cryogenic challenges like thermal contraction and modulus change.

cryoGS is a cryogenic geometric anti-spring vibration isolation system: a compact passive vertical vibration isolator that implements the geometric anti-spring (GAS) principle inside a cryostat and is explicitly tuned to work at cryogenic temperature. It is a monolithic radial blade GAS filter in which both the isolator and the suspended payload remain cold, rather than suspending a cold experiment from a warm stage through thin thermal links. The system was developed for cryogenic experiments that require both low temperature and extremely low vibration, particularly where closed-cycle cryostats based on pulse-tube or Gifford–McMahon coolers inject strong low-frequency motion starting at about $1\ \mathrm{Hz}$. In the reported experiment, cryoGS reached a vertical resonance frequency of $185\ \mathrm{mHz}$ at $7\ \mathrm{K}$, low enough to reduce vibration at the problematic $1\ \mathrm{Hz}$ cooler frequency by about an order of magnitude (Feenstra et al., 10 Sep 2025).

1. Scientific context and motivation

The motivation for cryoGS is specific to modern dry cryogenic instrumentation. Applications such as scanning probe microscopy, ultrasensitive force sensing, large-mass quantum mechanics, and cryogenic gravitational-wave instrumentation require the simultaneous attainment of low temperature and very low mechanical vibration. Closed-cycle cryostats are increasingly used because liquid helium is scarce and expensive, but pulse-tube and GM coolers inject strong low-frequency vibration into the cold stages. In the reported GM cryostat, the 4 K plate shows vibration levels orders of magnitude larger when the cooler is running, dominated by a peak at about $1\ \mathrm{Hz}$ and its harmonics (Feenstra et al., 10 Sep 2025).

This frequency range is difficult for conventional passive isolation. For an ordinary mass-spring suspension, lowering the resonance requires either a very soft spring or a very large mass. In a conventional vertical spring under gravity, that implies large static extension. The authors note that a $0.5\ \mathrm{Hz}$ classical mass-spring system would require about 1 m of spring extension under load, which is impractical inside a cryostat. cryoGS addresses this constraint by obtaining sub-hertz vertical resonance in a compact geometry.

A central engineering choice is that the entire filter operates cold. The design intentionally avoids keeping the isolator warm and suspending the cryogenic payload by a thin wire with separate thermalization links. This suggests a system-level preference for eliminating thermal-link vibration shortcuts and reducing mechanical complexity at the cryostat interface.

2. Geometric anti-spring principle

cryoGS applies the standard GAS concept in a cryogenic setting. A geometric anti-spring combines a load-bearing vertical restoring stiffness with a negative stiffness contribution generated by compressed springs acting perpendicular to the direction of motion. In the pedagogical two-dimensional model used in the paper, a vertically moving mass is supported by a vertical spring and opposed by two horizontally compressed springs. Near equilibrium, vertical displacement changes the geometry of the compressed side springs so that they push the mass further away from equilibrium, thereby reducing the net vertical stiffness (Feenstra et al., 10 Sep 2025).

The total vertical force is written as

$$F = k_y (l_y - (y-y_0)) + k_x (l_x-l_{x,0}) \sin(\theta)$$

$$= \left(k_y + k_x \left(1-\frac{l_{x,0}}{l_x} \right)\right) (l_y-(y-y_0))\text{,}$$

and the resulting effective spring constant is

$$k_\text{eff}(y)= k_y + k_x \left(1-\frac{l_{x,0}}{\sqrt{(l_y - (y-y_0))^2 + x_0^2}} \right)\text{.}$$

The tuning parameter is the compression $x_0$. By changing it, the anti-spring contribution can be made large enough that $185\ \mathrm{mHz}$0 becomes very small while the blades still carry the full payload. The ideal operating point is where the S-curve—equilibrium position versus load—is steepest, corresponding to minimum stiffness. If compression is too small, the filter remains in an undercompressed regime and stays relatively stiff. If compression is too large, the system enters an overcompressed regime in which $185\ \mathrm{mHz}$1 becomes negative over part of the range, the device becomes bistable, and snap-through occurs between two stable positions. The same proximity to instability that gives GAS filters their sub-hertz compactness also makes them narrow-band in tuning and strongly nonlinear.

The paper also embeds the tuned effective stiffness into suspended-filter transmissibility theory. For the base-excited mass-spring system, including viscous damping, structural loss, and the center-of-percussion effect, the equation of motion is

$185\ \mathrm{mHz}$2

with transfer function

$185\ \mathrm{mHz}$3

In the ideal undamped, massless-spring limit, transmissibility falls as $185\ \mathrm{mHz}$4 above resonance. In real blade systems, this decay is limited by blade mass through the center-of-percussion term.

3. Mechanical design and cryogenic integration

The realized device is a monolithic radial blade GAS. It consists of six quasi-triangular blade springs arranged radially in a horizontal spring plate. Each blade is clamped at its outer end in its own movable base block, while the inner ends converge to a central key stone from which the payload is suspended. Under load, the blades are bent nearly uniformly, approximating a constant-curvature profile. The radial geometry includes slits in the spring plate so that each blade base can be shifted inward or outward to tune the compressive preload (Feenstra et al., 10 Sep 2025).

Blade design is treated as a compromise among shape, material, and size. The blades follow the shape proposed to approximate constant curvature while allowing access to the low-stiffness regime, with profile

$185\ \mathrm{mHz}$5

and coefficients

$185\ \mathrm{mHz}$6

The implemented blades have base width $185\ \mathrm{mHz}$7, length $185\ \mathrm{mHz}$8, and are made from $185\ \mathrm{mHz}$9-thick grade 5 titanium (Ti-6Al-4V). Titanium was chosen because of its high yield strength—above $7\ \mathrm{K}$0—and suitable cryogenic mechanical properties. In the tuned geometry, each blade leaves the base at $7\ \mathrm{K}$1 and meets the key stone at $7\ \mathrm{K}$2 relative to the horizontal.

The suspended payload is roughly $7\ \mathrm{K}$3, realized as a cylindrical copper block with added copper disks and laboratory weights for coarse loading. The mass hangs below the spring plate, connected to the key stone by a rigid bronze rod through a central hole in the plate.

The cryogenic platform is a custom home-built fast-turnover GM cryostat centered on an RDK-408D2 cooler, specified as 40 W at 40 K and 1 W at 4 K, with cooldown to base temperature in under 24 h and heater power of 450 W for rapid warm-up. The cryostat provides a cold volume about 35 cm in diameter and 40 cm high, open from above at the 4 K plate. The GAS spring plate is mounted above the 4 K plate on three copper pillars, with the payload hanging below.

Thermalization of the suspended mass is a distinct cryogenic design problem because the titanium blades conduct heat poorly. If cooling relied only on the blades, turnaround time would become very long. The implemented solution is a mechanical clamp actuated by a helium-gas-driven bellows, operated between 0.5 and 1.5 bar. During cooldown and warm-up, the clamp presses the suspended mass against the 4 K plate to improve thermalization; once cold, the mass is released so the anti-spring suspension functions normally. This clamp is one of the most cryogenic-specific engineering elements of cryoGS.

4. Working-point tuning and cryogenic retuning

Operation near minimum stiffness requires precise tuning of both load and blade compression. The main diagnostic is the S-curve, a position-load plot of the suspended mass. Its inverse slope at the working point corresponds to the effective stiffness, so tuning seeks a nearly vertical S-curve. Vertical position is measured with a linear capacitive sensor read out by a lock-in amplifier. The sensor uses two concentric partially overlapping brass tubes, one attached to the spring plate and the other to the key stone; motion changes their overlap and therefore their capacitance (Feenstra et al., 10 Sep 2025).

Coarse load tuning is done by changing the physical payload mass. Fine in-situ load tuning is provided by a vertically oriented voice-coil actuator that pushes the mass slightly up or down, with calibration 85 mg/mA equivalent load change. Near the operating point the sensitivity is extreme: the authors state that a few grams are enough to double the resonance frequency, and the 7 K S-curve shows that sub-gram tuning precision is required. In situ S-curves are therefore recorded by sweeping the voice-coil current.

Compression tuning is mechanical. Each blade base is clamped between two brass blocks and can slide radially along slits in the spring plate. A tangential plate at the outer edge carries a fine-threaded adjustment screw with 0.5 mm/turn pitch that pushes the base inward against the outward spring force. The adjustment resolution is 20 $7\ \mathrm{K}$4m, corresponding to 1/24 turn. The working point is sharp enough that differences of less than 100 $7\ \mathrm{K}$5m in compression can turn a near-zero-stiffness filter bistable or noticeably increase the resonance.

Cryogenic retuning is required because room-temperature settings do not translate directly to low temperature. Two thermal effects are identified. First, the Young’s modulus of grade-5 titanium increases by about 10% from ambient to cryogenic temperature, increasing blade force. Second, differential thermal contraction between the titanium blades and the aluminum spring plate shifts the effective compression. The estimated relative contraction difference is $7\ \mathrm{K}$6, corresponding to about $7\ \mathrm{K}$7 motion of the spring bases. To compensate, before cooldown the authors deliberately reduce compression by $7\ \mathrm{K}$8—half a turn of the fine screw—as a first estimate of the cryogenic optimum, then iteratively remeasure cryogenic S-curves, warm up, adjust, cool down, and repeat.

This retuning procedure also clarifies a common misconception. The novelty is not the abstract anti-spring principle itself; GAS filters were already established mainly at room temperature. The distinctive contribution of cryoGS is that the low-stiffness point can be found, recovered, and operated in situ at cryogenic temperature, despite changes in modulus, contraction, and working-point load.

5. Measured performance and vibrational behavior

The tuning procedure succeeds at low temperature. At $7\ \mathrm{K}$9, cryoGS shows a near-zero-stiffness S-curve and a minimum measured vertical resonance of $1\ \mathrm{Hz}$0 (Feenstra et al., 10 Sep 2025). The authors also examine temperature dependence using heaters on the spring plate. Because titanium conducts heat poorly, tens-of-kelvin gradients can occur along the blades, so working-point quantities are plotted against the average temperature of both spring ends. Over the investigated low-temperature range, the working-point stiffness varies by only about 10%, while the working-point load shifts by tens of grams. The reported conclusion is that cryoGS performance is stable below about $1\ \mathrm{Hz}$1, provided the voice-coil has enough range to shift the operating point onto the new working-point load.

Vibration measurements use Geospace GS-ONE-LF geophones as vertical inertial sensors. These have a resonance at 4.5 Hz, so the experiment compensates them with a custom analog second-order correction filter to obtain an approximately linear velocity response. The corrected calibration is $1\ \mathrm{Hz}$2 for $1\ \mathrm{Hz}$3. One geophone monitors the 4 K plate and another the suspended mass. Average spectra are computed by Fourier transforming a 2000 s time series in 100 s windows spaced by 50 s.

The measured spectrum identifies several dynamical features. The first and intended mode is the vertical resonance at $1\ \mathrm{Hz}$4. Above that, the device attenuates vertical motion. At the cryostat’s problematic $1\ \mathrm{Hz}$5 forcing frequency, the low resonance allows reduction of vibration by an order of magnitude. A second mode appears at $1\ \mathrm{Hz}$6 and is attributed to pendulum motion of the suspended payload; from the simple pendulum relation, the inferred pendulum length is about 10 cm, consistent with the distance from the center of mass to the key stone pivot. Around 10 Hz, additional resonant features appear and are suggested to be torsional or rolling modes that break ideal symmetry and load the blades asymmetrically.

The transmissibility roll-off is also limited by distributed blade mass. For monolithic GAS filters, the center-of-percussion coefficient $1\ \mathrm{Hz}$7 is typically between $1\ \mathrm{Hz}$8 and $1\ \mathrm{Hz}$9 depending on blade geometry. In this device, the total blade mass is about 60 g, which is estimated to cause saturation of the $1\ \mathrm{Hz}$0 decay above roughly 5 Hz.

6. Limitations, related systems, and significance

cryoGS inherits the standard GAS tradeoffs while adding cryogenic-specific constraints. Operation near zero stiffness makes the device highly sensitive to small load and compression changes; too much compression produces bistability; the useful operating region is narrow; and the reduction of vertical stiffness leaves the system susceptible to tilt, cross-coupling, and symmetry-breaking rotational modes. A single GAS stage also provides little horizontal isolation. The measured $1\ \mathrm{Hz}$1 pendulum mode and the additional resonances around 10 Hz show that the demonstrated system is not yet a complete vibration-isolation platform (Feenstra et al., 10 Sep 2025).

The paper therefore frames several extensions. It suggests adding inverted pendulums for low-frequency horizontal filtering, as done in gravitational-wave isolation systems such as KAGRA and Virgo. KAGRA’s Type-A suspension uses a geometric anti-spring filter on an inverted pendulum table, followed by three standard GAS filters, a bottom GAS filter, and a cryogenic payload, with GAS filters providing vertical isolation and the inverted pendulum table providing horizontal isolation (collaboration et al., 2019). cryoGS differs from that architecture in scale and purpose: rather than being part of a kilometer-scale suspension chain, it is a compact cryogenic vertical filter intended to sit directly inside a closed-cycle cryostat.

A further limitation is the center-of-percussion ceiling from blade mass. The authors note that prior work has shown center-of-percussion compensation can improve high-frequency attenuation, and they also mention the possibility of active control to damp the low vertical resonance amplitude. More generally, a plausible implication is that cryoGS is best understood as the successful cryogenic transplantation of one stage of gravitational-wave-style vertical isolation into a compact cryostat-compatible format, rather than as a stand-alone full six-degree-of-freedom solution.

The significance of cryoGS lies primarily in implementation and methodology. GAS filters with vertical resonances of a few hundred millihertz or below were already known, but not as compact filters designed to operate directly at cryogenic temperature in a closed-cycle cryostat. Previous cryogenic vibration-reduction strategies often relied on bellows, remote exchange-gas cooling, flexible thermal links, or suspended room-temperature stages with thermal wiring. cryoGS instead keeps the entire isolation system at base temperature while still obtaining a sub-200 mHz vertical resonance in a compact package. For cryogenic scanning probe microscopy, ultrasensitive force sensing, large-mass quantum mechanics, and future cryogenic gravitational-wave payloads, the principal result is clear: a geometric anti-spring can be tuned and operated in situ at cryogenic temperature, and when so tuned it can provide meaningful attenuation of the strong $1\ \mathrm{Hz}$2 vibration produced by closed-cycle cryostats (Feenstra et al., 10 Sep 2025).