This protocol presents the operation and principles of micron-scale cylindrical and planar cryogenic liquid jets. Until now, this system has been used as a high repetition rate target in laser-plasma experiments. Anticipated cross-disciplinary applications range from laboratory astrophysics to material science, and eventually next-generation particle accelerators.
This protocol presents a detailed procedure for the operation of continuous, micron-sized cryogenic cylindrical and planar liquid jets. When operated as described here, the jet exhibits high laminarity and stability for centimeters. Successful operation of a cryogenic liquid jet in the Rayleigh regime requires a basic understanding of fluid dynamics and thermodynamics at cryogenic temperatures. Theoretical calculations and typical empirical values are provided as a guide to design a comparable system. This report identifies the importance of both cleanliness during cryogenic source assembly and stability of the cryogenic source temperature once liquefied. The system can be used for high repetition rate laser-driven proton acceleration, with an envisioned application in proton therapy. Other applications include laboratory astrophysics, materials science, and next-generation particle accelerators.
The goal of this method is to produce a high-speed, cryogenic liquid flow consisting of pure elements or chemical compounds. Since cryogenic liquids evaporate at ambient temperature and pressure, residual samples from operation at high repetition rates (e.g., 1 kHz) can be entirely evacuated from the vacuum chamber1. Based on the initial work by Grisenti et al.2, this system was first developed using cryogenic hydrogen for high intensity laser-driven proton acceleration3. It has subsequently been extended to other gases and used in a number of experiments, including: ion acceleration4,5, answering questions in plasma physics such as plasma instabilities6, rapid crystallization and phase transitions in hydrogen7 and deuterium, and meV inelastic X-ray scattering8 to resolve acoustic waves in argon in the Matter in Extreme Conditions (MEC) instrument at the Linac Coherent Light Source (LCLS)9.
Until now, other alternative methods have been developed to generate high repetition rate solid cryogenic hydrogen and deuterium samples. Garcia et al. developed a method in which hydrogen is liquefied and solidified in a reservoir and extruded through an aperture10. Due to the high pressure required for extrusion, the minimum sample thickness demonstrated (to date) is 62 µm11. This system also exhibits large spatial jitter12. More recently, Polz et al. produced a cryogenic hydrogen jet through a glass capillary nozzle using a sample gas backing pressure of 435 psig (pounds per square inch, gauge). The resulting 10 µm cylindrical jet is continuous but appears highly rippled13.
Presented here is a method that produces cylindrical (diameter = 5-10 µm) and planar jets with various aspect ratios (1-7 µm x 10-40 µm). The pointing jitter increases linearly as a function of distance from the aperture5. Fluid properties and the equation of state dictate the elements and chemical compounds that can be operated in this system. For example, methane cannot form a continuous jet due to Rayleigh breakup, but it can be used as droplets14. Moreover, the optimal pressure and temperature conditions vary significantly among aperture dimensions. The following paragraphs provide the theory needed to produce laminar, turbulent-free cryogenic hydrogen jets. This can be extended to other gases.
The cryogenic jet system consists of three main subsystems: (1) sample gas delivery, (2) vacuum, and (3) cryostat and cryogenic source. The system depicted in Figure 1 has been designed to be highly adaptable for installation in different vacuum chambers.
The gas delivery system is comprised of an ultra-high purity compressed gas cylinder, gas regulator, and mass flow controller. The backing pressure of the sample gas is set by the gas regulator, while the mass flow controller is used to measure and restrict the gas flow delivered to the system. The sample gas is first filtered in a liquid nitrogen cold trap to freeze out contaminant gases and water vapor. A second in-line particulate filter prevents debris from entering the final segment of the gas line.
Turbomolecular pumps backed with high pumping speed scroll pumps maintain high vacuum conditions in the sample chamber. The chamber and foreline vacuum pressures are monitored using vacuum gauges V1 and V2, respectively. It should be noted that operating the cryogenic jet introduces a substantial gas load (proportional to the total sample flow) into the vacuum system when the liquid vaporizes.
A proven method to reduce the gas load is to capture the residual liquid before bulk vaporization can occur. The jet catcher system consists of an independent vacuum line terminated by an ø800 µm differential pumping aperture located up to 20 mm from the cryogenic source cap. The line is evacuated with a pump that exhibits optimal efficiency in the 1 x 10-2 mBar range (i.e., a roots blower vacuum pump or hybrid turbomolecular pump) and is monitored by a vacuum gauge V3. More recently, the catcher has allowed cryogenic hydrogen jets of up to 7 µm x 13 µm to be operated with two orders of magnitude improvement to the vacuum chamber pressure.
A fixed length, continuous flow liquid helium cryostat is used to cool the source to cryogenic temperatures. Liquid helium is drawn from a supply dewar using a transfer line. The return flow is connected to an adjustable flowmeter panel to regulate the cooling power. The temperature of the cold finger and cryogenic source is measured with four lead silicon diode temperature sensors. A proportional-integral-derivative (P-I-D) temperature controller delivers variable voltage to a heater installed near the cold finger to adjust and stabilize the temperature. The sample gas enters the vacuum chamber through a custom feedthrough on the cryostat flange. Inside the chamber, the gas line wraps around the cryostat to precool the gas before connecting to a fixed gas line on the cryogenic source assembly. Stainless steel screws and a 51 µm thick layer of indium thermally seal the cryogenic source to the cold finger.
The cryogenic source (Figure 2) consists of six main components: a (1) sample gas line, (2) source body, (3) source flange with in-line particulate filter, (4) aperture, (5) ferrule, and (6) cap. The source body contains a void, which acts as the sample reservoir. A threaded Swagelok sintered 0.5 µm stainless steel filter prevents any debris or solidified contaminants from entering the liquid channel and obstructing the aperture. A thicker, 76 µm thick indium ring is placed between the aperture and liquid channel to increase the deformation length and reliably seal the aperture. When the cap is threaded onto the source flange, the indium is compressed to form a liquid and thermal seal. The ferrule and source cap center the aperture during installation.
There are a number of overall considerations in the initial design of a system for cryogenic liquid jets operated in the continuous, laminar regime. Users must estimate the total cooling power of the cryostat, thermal properties of the cryogenic source design, vacuum system performance, and liquid temperature and pressure. Provided below is the theoretical framework required.
Cooling power considerations
1) Liquefying hydrogen15: the minimum cooling power required to liquify hydrogen from 300 K to a temperature can be roughly estimated using the following equation:
Where: is the specific heat at constant pressure , and the latent heat of vaporization of H2 at the pressure-dependent liquefaction temperature . For instance, a cryogenic hydrogen jet operated at 60 psig gas pressure and cooled down to 17 K requires a minimum of 4013 kJ/kg. With a hydrogen gas flow of 150 sccm (standard cubic centimeters per second), this corresponds to a heat of 0.9 W.
It should be noted that the liquefaction process contributes only one-tenth of the total cooling power required. To reduce the heat load on the cryostat, the gas can be precooled to an intermediate temperature before entering the source body.
2) Radiative heat: to maintain the cryogenic source at a temperature , the cryostat needs to compensate for radiative heating. This can be estimated by balancing the difference of emitted and absorbed blackbody radiation using the following equation:
Where: A is the area of the source body, is the Stefan-Boltzmann constant, and is the temperature of the vacuum chamber. For example, a typical jet source of A = 50 cm2 cooled down to 17 K requires a minimum cooling power of 2.3 W. can be locally decreased by adding an actively cooled radiation shield covering a substantial part of the cryogenic source.
3) Residual gas conduction: although thermal radiation is dominant in ultra-high vacuum conditions, the contribution due to conduction in the residual gas becomes non-negligible during jet operation. The liquid jet introduces substantial gas load in the chamber, resulting in an increase in vacuum pressure. The net heat loss from thermal conduction of the gas at a pressure p is calculated using the following equation:
Where: is a coefficient depending on the gas species (~3.85 x 10-2 W/cm2/K/mBar for H2), and is the accommodation coefficient that depends on the gas species, geometry of the source, and temperature of the source and the gas16,17. When operating a cryogenic hydrogen jet at 17 K, assuming a cylindrical geometry of the source and that hydrogen is the main gas present in the vacuum chamber, gas conduction generates heat that can be estimated using the following equation:
For example, gas conduction at a vacuum pressure of 4.2 x 10-3 mBar generates as much heat as thermal radiation. Therefore, the vacuum pressure is generally kept below 1 x 10-3 mBar during jet operation, adding a ~0.55 W heat load to the system (A = 50 cm2).
The gas load introduced in the chamber during operation is obtained by the flow of the cryogenic jet. The resulting vacuum pressure is then determined by the effective pumping speed of the vacuum system and volume of the vacuum chamber.
To operate the cryogenic jet, the cryostat has to generate sufficient cooling power to compensate for the different heat sources above (e.g., 3.75 W), not including the heat losses of the cryostat system itself. Note that the cryostat efficiency also strongly depends on the desired cold finger temperature.
Estimating jet parameters
To establish continuous laminar flow, several conditions must be satisfied. For brevity, the case of a cylindrical liquid flow is shown here. The formation of planar jets involves additional forces, resulting in a more complex derivation that is beyond the scope of this paper18.
1) Pressure-speed relationship: for incompressible liquid flows, conservation of energy yields the Bernoulli equation, as follows:
Where: is the fluid atomic density, is the fluid velocity, is gravitational potential energy, and p is the pressure. Applying the Bernoulli equation across the aperture, the functional relationship between the jet velocity and sample backing pressure can be estimated using the following equation:
2) Jet operation regime: the regime of a cylindrical liquid jet can be inferred using the Reynolds and the Ohnesorge numbers. The Reynolds number, defined as the ratio between the inertial and viscous forces within the fluid, is calculated using the following equation:
Where: , , , and are the density, speed, diameter, and dynamic viscosity of the fluid, respectively. Laminar flow occurs when the Reynolds number is less than ~2,000. Similarly, the Weber number compares the relative magnitude of the inertia to the surface tension and is calculated using the following equation:
Where: σ is the surface tension of the liquid. The Ohnesorge number is then calculated as follows:
This velocity-independent quantity is used in combination with the Reynolds number to identify the four liquid jet regimes: (1) Rayleigh, (2) first wind-induced, (3) second wind-induced, and (4) atomization. For laminar turbulent-free cryogenic liquid flow, parameters should be selected to operate within the Rayleigh regime19 (i.e., ). In this regime, the fluid column will remain continuous with a smooth surface until the so-called intact length, estimated as follows20 :
The different fluid parameters for a 5 µm diameter cylindrical cryogenic hydrogen jet operated at 60 psig and 17 K are summarized in Figure 3. To maintain a continuous jet for longer distances, the liquid must be cooled sufficiently close to the liquid-solid phase transition (Figure 4) so that evaporative cooling, occurring once the jet propagates in vacuum, solidifies the jet before the onset of Rayleigh breakup3,21.
The following protocol details the assembly and operation of a 5 µm diameter cylindrical cryogenic hydrogen jet operated at 17 K, 60 psig as an example case. An extension of this platform to other aperture types and gases requires operation at different pressures and temperatures. As a reference, working parameters for other jets are listed in Table 1. Sections 1-3 and section 7 are performed at ambient temperature and pressure, while sections 4-6 are performed at high vacuum.
1. Installation of the cryostat in the vacuum chamber
CAUTION: A vacuum vessel can be hazardous to personnel and equipment from collapse, rupture due to back-fill pressurization, or implosion due to vacuum window failure. Pressure relief valves and burst disks must be installed on vacuum vessels within a cryogenic system to prevent over-pressurization.
2. Installation of the cryogenic source components
NOTE: All preparation and assembly of the cryogenic source components should be performed in a clean environment with the appropriate cleanroom clothing (i.e., gloves, hairnets, lab coats, etc.).
3. Installation of aperture
4. Cool-down procedure
5. Liquefication and jet operation
6. Warm-up procedure
NOTE: If the aperture is damaged during operation, immediately limit the sample gas flow to 10 sccm and reduce the sample gas pressure to 30 psig. Then, proceed directly to step 6.5.
7. Replacement of aperture
Following step 5.4, high magnification shadowgraphs are used to assess laminarity, positioning jitter, and long-term stability during jet operation. It is critical to use pulsed, sub-nanosecond illumination to record an instantaneous image of the jet so that the jet motion (~0.1 µm/ns for H2) does not blur surface irregularities or turbulence. Sample images of 2 x 20 µm2 H2, 4 x 12 µm2 H2, and 4 x 20 µm2 D2 jets are shown in Figure 5.
An additional high magnification imaging system is used to precisely position the cryogenic liquid jet in space. For simplicity, the imaging systems are designed to provide front and side views of the jet. It is particularly important to assess the jet stability and determine the orientation of the planar jets. A study of the spatial jitter of a 2 x 20 µm2 H2 as a function of distance from the aperture, performed during a single test over several hours, is shown in Figure 6. The 1σ positioning jitter for each datapoint in Figure 6A was calculated from 49 images recorded at 10 Hz. Here, the jet position was determined relative to a fixed reference position. Figure 6B shows the normalized histograms of the jet position at 23 mm as an example. A more detailed study can be found in Obst et al.5. On average, the spatial jitter increases linearly away from the nozzle.
Typical system observables during liquefying and jet operation (according to section 5) of a 4 x 20 µm2 cryogenic deuterium jet are shown in Figure 7. Careful monitoring of the temperature, flow, sample backing pressure, and vacuum pressures allows the operator to quickly identify any irregularities and react accordingly. For example, if the jet leaves the catcher, indicated by a dashed box, the vacuum chamber and foreline pressure increase significantly. Additional cooling power is then needed to maintain the setpoint temperature.
Once stabilized, all observables should be constant with minimal oscillations. Any long-term drift is indicative of a problem (e.g., leaks, gas contamination, decrease in vacuum system performance, positioning drift in catcher). The choice of aperture strongly dictates the operational parameters of the jet in the Rayleigh regime. Once the optimal parameters are identified for a given gas and aperture type, the resulting jet is highly reproducible; however, any minor deviations in the aperture require reoptimization starting from the previously identified values. Typical operation parameters are summarized in Table 1.
Figure 1: P&ID diagram of a typical cryogenic liquid jet delivery platform. The sample gas, vacuum, and cryogenic subsystems are depicted. The vacuum chamber, turbomolecular pump foreline, and jet catcher foreline pressures are monitored with vacuum gauges V1, V2, and V3, respectively. The cryostat temperature is actively regulated using a P-I-D temperature controller. Please click here to view a larger version of this figure.
Figure 2: Three-dimensional exploded-view drawing of the cryogenic source assembly. Indium seals are installed between the cold finger and source body, source body and flange, and source flange and aperture. Please click here to view a larger version of this figure.
Figure 3: Summary of fluid dynamics parameters. Parameters are provided, assuming a ø5 µm cylindrical cryogenic hydrogen jet operated at 60 psig and 17 K. Values for density, viscosity, and surface tension are from NIST.15. Please click here to view a larger version of this figure.
Figure 4: Hydrogen equation of state at cryogenic temperatures15. The critical and triple points are indicated by blue and orange filled circles, respectively. Jet operation follows an isobar through the gas-liquid phase transition. The jet solidifies via evaporative cooling in the vacuum chamber. The grey box indicates the range of backing pressures (40-90 psia) and temperatures (17-20 K) which are scanned over to optimize the stability of a ø5 µm cylindrical cryogenic hydrogen jet. Please click here to view a larger version of this figure.
Figure 5: Representative 20x magnification shadowgraphs of turbulent-free, laminar cryogenic liquid jetsusing a 10 ps/1057 nm wavelength laser. (A) Aperture = 2 x 20 µm2, gas = H2, T = 15.8 K, P = 188 psig. (B) Aperture = 4 x 12 µm2, gas = H2, T = 17.2 K, P = 80 psig. (C) Aperture = 4 x 20 µm2, gas: D2, T = 20 K, P = 141 psig. Please click here to view a larger version of this figure.
Figure 6: Jet position stability for 2 x 20 µm2 cryogenic hydrogen jet. Parameters are 18 K, 60 psig, and Re 1887. (A) Positioning jitter as a function of distance from the aperture. The longitudinal (lateral) jitter corresponds to motion parallel to the short (long) axis of the rectangular sheet. (B) Normalized histogram of jet position to determine the lateral jitter (σ = 5.5 µm) and longitudinal jitter (σ = 8.5 µm) 23 mm from the nozzle. Please click here to view a larger version of this figure.
Figure 7: Representative flow and pressures during cryogenic jet operation. (A) Left: sample gas flow, right: sample gas backing pressure as a function of time. Semi-log plot of the vacuum chamber pressure (V1; B), turbomolecular pump foreline pressure (V2; C), and jet catcher pressure (V3; D) as functions of time. Circled numbers identify changes in the system observed during section 5 of the protocol. Please click here to view a larger version of this figure.
Sample gas | Aperture | Temperature (K) | Pressure (psig) | Flow (sccm) |
Hydrogen | ø5 µm cylindrical | 17 | 60 | 150 |
50% Hydrogen, 50% Deuterium | ø5 µm cylindrical | 20 | 30, 30 | 130 |
Deuterium | ø5 µm cylindrical | 22 | 75 | 80 |
Hydrogen | 1 µm x 20 µm planar | 18 | 182 | 150 |
Hydrogen | 2 µm x 20 µm planar | 18 | 218 | 236 |
Hydrogen | 4 µm x 20 µm planar | 17.5 | 140 | 414 |
Deuterium | 4 µm x 20 µm planar | 20.5 | 117 | 267 |
Argon | ø5 µm cylindrical | 90 | 50 | 18.5 |
Methane | ø5 µm cylindrical | 100 | 75 | 46 |
Table 1: Sample jet operation conditions.
Successful operation of the cryogenic liquid jet requires meticulous cleanliness and careful monitoring of temperature stability. One of the most frequent and avoidable failures is a partial or full blockage of the micron-sized aperture. Copper, stainless steel, or indium from the source or airborne particles can be introduced at any step of the source assembly. All components must undergo a robust cleaning process using indirect sonication. Assembly and storage in a Class-10,000 cleanroom or better improves the success rate.
Another critical step of the procedure is to stabilize the cryogenic source temperature. Users must ensure that the temperature of the liquid exiting the source is measured independently from the variable heat released by continuous liquefaction in the reservoir. This is accomplished by placing the temperature sensor near the aperture (e.g., on the source flange) or far from the heat source. Furthermore, P-I-D parameters must be manually optimized using the Ziegler-Nichols method for each combination of temperature and backing pressure. If the temperature fluctuations become too large, periodic oscillations can be observed on the jet sometimes leading to periodic breakup. It should be noted that built-in autotuning functions or low-pass filters have not been successful in stabilizing the temperature during jet operation.
The cryogenic liquid jet system, while highly adaptable, is challenging to implement at large-scale facilities with established vacuum protocols. For instance, differential pumping stages are required when upstream equipment is sensitive to the residual gas (e.g., FLASH free-electron laser at DESY or MeV-UED instrument at SLAC). In addition, large diameter vacuum chambers, such as those for multi-PW lasers, likely require in-vacuum flexible cryostats. Compared to conventional fixed length cryostats, they can be readily decoupled from chamber vibrations and have a shorter lever arm. A flexible in-vacuum cryostat has already been implemented with the Draco Petawatt laser at Helmholtz-Zentrum Dresden-Rossendorf (HZDR). Another observation is that the aperture can be damaged when the jet is irradiated by an ultra-high intensity laser too close to the source. Recently, a mechanical chopper blade (operating at 150 Hz and synchronized with the laser pulse) has been implemented to protect and isolate the aperture from the laser-plasma interaction.
This system produces micron-scale, highly tunable, turbulent-free, laminar cylindrical and planar cryogenic liquid jets. Ongoing development of the cryogenic liquid jet system is focused on advanced aperture materials and design, vacuum system and catcher improvements, and advanced hydrogen isotope mixing. This system will enable a transition to high repetition rate high energy density science and pave the way to the development of next-generation particle accelerators.
The authors have nothing to disclose.
This work was supported by the U.S. Department of Energy SLAC Contract No. DE- AC02-76SF00515 and by the U.S. DOE Office of Science, Fusion Energy Sciences under FWP 100182. This work was also partially supported by the National Science Foundation under Grant No. 1632708 and by EC H2020 LASERLAB-EUROPE/LEPP (Contract No. 654148). C.B.C. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC). F.T. acknowledges support from National Nuclear Security Administration (NNSA).
Cryogenic apron | Tempshield | Cryo-apron | Core body protection from cryogenic liquids |
Cryogenic face shield | 3M | 82783-00000 | ANSI Z87.1 rated for full face protection from cryogenic liquids |
Cryogenic gloves | Tempshield | Cryo-gloves MA | Hand protection from cryogenic liquids |
Cryogenic source components | SLAC National Accelerator Laboratory | Custom | Components are made of Oxygen-free Copper (OFC) to maximize thermal conductivity at cryogenic temperatures. |
Cryostat and transfer line | Advanced Research Systems | LT-3B | Available in custom lengths up to 1250 mm for compatibility with existing vacuum vessels. Transfer line length and style can be selected based on system or laboratory space constraints. |
Cylindrical apertures | SPI Supplies | P2005-AB | Commercial cylindrical apertures can be purchased individually |
Electronic-grade isopropanol | Sigma Aldrich | 733458-4L | 99.999%, minimal particulates/trace metals, dries residue free |
Flammable gas regulator | Matheson | M3816A-350 | Pressure control of sample gas (e.g. hydrogen, deuterium) |
Indium | Indium Corporation | Custom | 99.99%, 50-75µm thick, for thermal and liquid seals in cryogenic source |
Jet catcher system | SLAC National Accelerator Laboratory | Custom | Consists of skimmer, vacuum hardware and feedthroughs, vacuum gauge, roots vacuum pump |
Laboratory-grade acetone | Sigma Aldrich | 179973-4L | Used to remove grease and photoresist from components. Purity and grade not critical since final cleaning will use electronic-grade isopropanol |
Leak detector | Matheson | SEQ8067 | To ensure jet apertures have sealed before pumping down |
Liquid helium | Airgas | HE 100LT | Top-loading dewar, Consumption depends on cryostat, source dimensions, and total gas flow. Typically 3-5 L/h. |
Liquid nitrogen | Airgas | NI 160LT22 | Total cold trap volume 4 L, consumption approximately 2L/h during jet operation |
LN dewar flask (4 L) | ThermoFisher Scientific | 4150-4000 | For the liquid nitrogen cold trap |
LN transfer hose | Cryofab | CFUL series | Uninsulated cryogenic hose with a phase separator to transfer LN from storage dewar to LN dewar flask for the cold trap |
Manual XY manipulator | Pfeiffer Vacuum | 420MXY100-25 | Course adjustment (+/- 12.5 mm) of cryogenic source. |
Manual Z manipulator | McAllister Technical Services | ZA12 | Course adjustment of cryostat length for interchangeability on different vacuum vessels. Additionally, retracting cryogenic source from interaction point. |
Mass flow controller | MKS Instruments | P9B, GM50A | To control and monitor gas flow |
Planar apertures | Norcada | Custom | Custom nanofabrication of planar apertures |
Positioning actuators | Newport | LTAHLPPV6, 8303-V | High-precision (<2µm), motorized jet positioning |
Rotation stage | McAllister Technical Services | DPRF600 | Precision alignment of jet orientation |
Safety glasses | 3M | S1101SGAF | ANSI Z87.1 rated for work with compressed gases |