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We illustrate the benefits of a thin, low pressure helium cell for efficient and safe heat removal in cryogenically-cooled active mirror laser amplifiers operating in the [100 J-1 kJ] / [1-10 Hz] range. A homogeneous gain medium temperature distribution averaging 160 K is obtained with a sub-mm helium-filled gap between the gain medium and a copper plate at 77 K. A significant degree of flexibility for tuning the temperature in the amplifier can be achieved by varying the pressure of the helium gas in the 102 to 105 Pa range.
©2011 Optical Society of America
1. Introduction
Solid-state lasers delivering high average-powers find applications in a wide variety of fields, ranging from materials processing, remote sensing, free-space communications, laser particle acceleration, gravitational wave interferometry, to laser-driven inertial fusion. Properly engineering amplifier sections of such lasers requires careful consideration of Amplified Spontaneous Emission (ASE), the Laser Induced Damage Threshold (LIDT) of the optics, and thermal effects due to the pumping process. ASE and LIDT can be overcome by proper scaling of the laser gain medium, which, however, can result in an increase of thermal effects. The unavoidable heating associated with the pumping process differs for different materials and is related to various physical phenomena such as quantum defect, concentration quenching, upconversion, nonradiative sites, etc [1]. The heating of the laser gain medium leads to thermal gradients responsible for changes in the refractive index. When thermal gradients are severe enough, significant stresses and strains are induced in elastic laser materials, resulting in strain-induced distortion of the optical indicatrix and the surfaces. This degrades the output beam [2]. Ultimately, when surfaces are subjected to sufficiently high stress levels, thermally-induced fracture of the laser material occurs.
The increased performance of laser diodes as pump sources triggered interest in Yb3+ doped laser gain media, especially Yttrium Aluminum Garnet (YAG) and Calcium Fluoride (CaF2). Such interest is driven by the good thermo-mechanical properties and the availability in large sizes and different forms (crystals or ceramics) of these host materials. Diode-Pumped Solid-State Lasers (DPSSL) are the favored candidates for highly efficient, high energy laser systems operating at high repetition rates. The thermal, mechanical, and optical properties of those materials, however, vary strongly with temperature [3,4]. High average-power operation at room temperature requires relatively aggressive cooling techniques. Setting the operating temperature at much lower values (e.g. at cryogenic temperatures) not only relaxes the constraints in terms of heat extraction (better thermal conductivity), but it also strongly enhances laser amplifier performance (higher cross sections) [5]. It is therefore easier to design amplifiers with reduced thermally induced phase aberrations, stresses, and birefringence [6,7], which is a critical point for high average-power, high energy laser systems.
High energy DPSSL systems operating at several hertz repetition rates have been developed during the last decade at the Lawrence Livermore National Laboratory (LLNL, Livermore, USA) with the Mercury laser system delivering 61 J (10 Hz) [8], at the Institute for Laser Engineering (ILE, Osaka, Japan) with the HALNA laser system delivering 20 J (10 Hz) [9], at the Institute of Optics and Quantum Electronics at the Friedrich-Schiller University (IOQ, Jena, Germany) with the POLARIS system delivering 12 J (0.05 Hz) [10] and the Centre National pour la Recherche Scientifique (CNRS) Laboratoire pour l’Utilisation des Lasers Intenses at the Ecole Polytechnique (LULI, Palaiseau, France) with the Lucia system delivering 10 J (2 Hz) [11,12]. The amplifier architectures of these systems are based on multiple slab, zig-zag slab, rod and active mirror, respectively. The thermal management techniques differ as well, relying on high pressure helium flow, water cooling and thermal compensation with resistance heating, conductive radial cooling and backside water jet cooling. All of these systems were operated at room temperature. The improved material properties of the gain media at cryogenic temperatures will help mitigate the strong thermal effects expected in high average-power, high energy projects like HiPER [13], LIFE [14,15], and ELI [16]. These planned laser systems aim at delivering kilojoule picosecond and nanosecond pulse trains with repetition rates in the 10 Hz regime. The primary mission of HiPER and LIFE is laser-driven inertial fusion in the context of energy production, whereas ELI will focus on the exploitation of ultra-short and ultra-intense laser pulses.
The ~10% wall plug efficiency goal for fusion energy laser drivers requires significant improvement with respect to current state of the art laser technology. Thanks to increased values for the emission cross section of Yb3+ doped YAG and CaF2 at low temperatures, this efficiency requirement will become reachable when operating the amplifier at a target temperature in the 160 K region. Near this temperature, it is indeed possible to find a satisfying compromise between efficiency benefits and increased ASE related issues (e.g. parasitic oscillations). For continuous-wave (cw) operation, where ASE is much less critical, even lower temperatures can be used with innovative amplifier architectures like Total-Reflection Active-Mirror (TRAM) [17]. In this scheme, a YAG ceramic prism is cooled through direct contact with liquid nitrogen at 77 K, allowing a cw output power of 273 W with an optical efficiency of 65% [18].
Within the HiPER program, three DPSSL schemes are currently being explored in conjunction with 100 J level testbed prototypes [19]. All proposed prototypes rely on gain medium temperatures close to 160 K. The LULI laboratory, the IOQ and STFC’s (Science & Technology Facilities Council, UK) Central Laser Facility at Rutherford Appleton Laboratory [20] are operating these prototypes. At LULI we are currently upgrading the Lucia laser chain by adding a cryogenically cooled second power amplifier with the prospect of increasing the output energy by several tens of joules and demonstrating a new cooling concept relevant for HiPER.
In this paper, through numerical modeling, we calculate the volume temperature distribution of a Yb3+:YAG active mirror laser amplifier surrounded by an absorbing cladding material (Cr4+:YAG) at a target temperature near 160 K. Helium gas, sealed in a low pressure (<1 bar), sub-millimeter thin cell located at the High Reflectivity (HR) coated side of the active mirror, is used to transfer the heat from the gain medium to a copper heat sink at 77 K, as shown in Fig. 1 . This helps to ensure long term reliability of the HR coating by eliminating direct contact with the liquid coolant (as in the current Lucia first amplifier head), glue (industrial thin disks) or high velocity gas (Mercury scheme).
Fig. 1 Schematic view of the proposed cooling scheme for thermalization of a disk laser gain medium (top layer, pink) with a gas cell in contact with a cold heat sink. For the Lucia cryogenic amplifier design, typical foreseen values are: Yb3+:YAG at 160 K, copper heat sink in contact with a 77 K (liquid nitrogen temperature) dewar,102 to 105 Pa pressure of helium in a ~100 µm thick cell.
We have shown that radial thermal gradients can vanish when the absorbing cladding is properly designed to allow heat flow only in the direction perpendicular to the large faces of the active mirror. This study also revealed the critical role played by the helium gap thickness in the thermal management for such an approach. In addition, we have found that great flexibility can be obtained by adjusting the helium cell pressure in the 500 to 5000 Pa range, thus providing an efficient tunable thermal management technique.
2. Helium thermal conductivity dependence with cell pressure and geometry
Helium thermal conductivity dependence with temperature, pressure and geometry is derived from the kinetic gas theory and heat transport perpendicular to a thin gap, as described in [21,22]. It can then be expressed by:
where kbulk (T) is the helium bulk conductivity, R is the specific gas constant for helium, e and p are the thickness and pressure of the helium gas cell, and α1 and α2 are the thermal accommodation factors. The thermal accommodation factor represents the process of energy exchange at the solid-gas interface in a low-density-gas environment. We use a thermal accommodation factor value of 0.4 for both surfaces in contact with helium at temperatures varying between 50 K and 300 K [23,24]. Figure 2 illustrates the helium thermal conductivity dependence with temperature in the range 50 K to 300 K, at a pressure of 104 Pa, and for helium thicknesses of 50 μm, 100 μm, 150 μm, 200 μm, and 1 mm.Fig. 2 Thermal conductivity of helium as a function of temperature and thickness for α1 = α2 = 0.4. The pressure is fixed at 104 Pa. Curves from top to bottom are bulk, 1 mm, 200 μm, 150 μm, 100 μm and 50 μm helium thickness.
We note that k is decreasing not only with the temperature, but also with the cell thickness. It is also strongly dependent on pressure, as shown in Fig. 3 , where the k dependence with temperature in a 100 μm thick He cell is given for pressures of 102 Pa, 103 Pa, 104 Pa and 105 Pa (~1 atm).
Fig. 3 Thermal conductivity of helium as a function of temperature and pressure for α1 = α2 = 0.4. The thickness is fixed at 100 μm. Curves from top to bottom are obtained for 105 Pa (~1 atm), 104 Pa, 103 Pa and 102 Pa helium pressure.
Finally, Fig. 4 shows the variation of thermal conductivity of helium over a wide range of pressures for thicknesses of 100 μm, 150 μm, and 200 μm. Plain and dashed lines give the variation of k at temperatures of 160 K and 300 K, illustrating the potential of such a cooling approach not only for cryogenic temperatures but also for room temperature operation. These curves demonstrate that small adjustments of thickness and/or pressure of a thin cell containing low pressure helium are suitable for accurate thermalization of a laser gain medium.
Fig. 4 Thermal conductivity of helium as a function of pressure for temperatures of 160 K (plain lines) and 300 K (dashed lines). Curves from top to bottom are obtained for 200 μm, 150 μm, and 100 μm helium gap thicknesses.
Another set of curves (Fig. 5 ) illustrates this approach by displaying the slab HR surface temperature for several values of pressure and cell thickness, when the heat flux is q = 5 W/cm2. This flux is close to what must be evacuated with the current active-mirror amplifier operating at room temperature on Lucia. In this amplifier, 8.7 W/cm3 are stored in a 7 mm thick YAG disk leading to an average 6.1 W/cm2 heat flux being transferred through the cooled face. For the laser gain medium operating at 160 K, a 5 W/cm2 flux is associated with a 5 Hz repetition rate operation. As an illustration, in order to thermalize a gain medium near 160 K with a 100 µm thick cell (green line in Fig. 5), a pressure of 3000 Pa (30 mbar) is required. The relationship between the heat flux, the pressure and both helium cell surface temperatures is derived from Y. Demirel and S.C. Saxena [25]. The Knudsen number, Kn, is defined as the ratio between Λ, the mean-free-path of the gas molecules, and L, the gas cell thickness, i.e. Kn = Λ/L. In our configuration, we fall in the so-called intermediate or transition regime where 0.1 < Kn < 10. The heat flux Q between the two parallel cell surfaces can be approximated by 1/Q = 1/QFM + 1/QC, where QFM is the heat flux in the free molecular case (Kn > 10) and QC is the heat flux in the continuous regime (Kn < 0.01), as defined in Ref [25]. A complementary perspective, shown in Fig. 6 , helps to illustrate the flexibility offered by pressure adjustment.
Fig. 5 Slab HR surface temperature as a function of He gas pressure and thickness for heat flux of 5 W/cm2. The other surface temperature is set to 77 K. The thermal accommodation factor values are 0.4.
Fig. 6 Heat flux transferred between a laser gain medium at 160 K and a copper heat sink at 77 K versus the helium cell pressure for 50 μm, 100 μm, and 200 μm helium gap thickness.
During the operation of a high average power DPSSL, it is often necessary to change the repetition rate and the associated thermal load in the gain medium. In doing so, it is difficult to maintain the same laser properties, in particular the energy and the beam quality. To achieve this, it is desirable to keep the amplifier gain medium at the same target temperature, i.e. to maintain temperature dependent cross sections and thermally induced stresses at the same levels. Figure 6 shows the heat flux between a 77 K cooled plate and a 160 K (target temperature) gain medium as a function of pressure for three values of cell thickness. For instance, we observe that for a 50 µm thick cell (brown line), 4000 Pa pressure is required when operating the laser at 10 Hz (i.e. 10 W/cm2 heat flux). Note that only 700 Pa and 100 Pa are required for 5 Hz (i.e. 5 W/cm2) and 1 Hz (i.e. 1 W/cm2) operation, respectively. This technique could also be used for thermalization of a laser gain medium at room temperature, as illustrated in Fig. 7 . This figure displays the heat flux transferred between the laser gain medium at 293 K and a copper heat sink in contact with two different coolants versus the helium cell pressure. The solid curves are for liquid Nitrogen (LN2) at 77 K for three different cell thicknesses, whereas the dashed curves are for a copper heat sink in contact with water at 280 K. The water cooling could be used only if low values of heat transfer are allowed.
Fig. 7 Heat flux transferred between a laser gain medium at room temperature (293 K) and a copper heat sink cooled with LN2 at 77 K (plain curves) or with H2O at 280 K (dashed curves) versus the helium cell pressure for three different cell thicknesses.
3. Amplifier gain medium geometry and heat load
For efficient thermal management of active mirror amplifiers, geometrical constraints like the aspect ratio of the gain medium and additional heat contributions (absorption of the ASE in an optional cladding or heating of the gain medium mount, for instance) must be considered. As we have demonstrated experimentally, such optimization cannot be decoupled from ASE management [26]. With a YAG host matrix, one could utilize a disk that is a composite structure with diameter of 7.44 cm and thickness of 1.44 cm. A 2 cm wide peripheral layer of 0.03 at.% Cr4+ doped YAG acts as a cladding material and ASE sink to suppress parasitic lasing. Such structures are readily available with co-sintered ceramics, as can be seen in a slightly smaller example pictured in Fig. 8 . The ~100 µm helium cell and the 77 K copper mount are also sketched. Table 1 gives the pump, geometry, and cooling parameters used in the finite-element model to estimate the volume-temperature distribution.
Fig. 8 Illustration of the composite Cr4+/Yb3+:YAG Lucia disk amplifier with a low pressure helium cell located on the HR coated side (an already commissioned 4.5 cm sample is pictured as well with the Cr4+ doped periphery).
Table 1. Pump, Geometry and Cooling Parameters Used in the Finite-element Model
It is estimated that 45% (86 W) of the total pump power is absorbed within the cladding through spontaneous emission. Only 10% (19 W) is localized in the Yb3+ doped pumped central area. Such a ratio would occur in the worst case scenario for thermal management when no laser extraction takes place.
The remaining 45% of the power is associated with spontaneous emission in the pump direction. The temperature dependence of the thermal conductivity of YAG was considered [27], while copper thermal conductivity at 77 K was taken to be 400 W/(m-K).
Axial and radial temperature profiles in the Lucia amplifiers are estimated with a Finite Element Model (FEM). Let us consider the heat transport equation ∇[k(T)∙∇T(x,y,z)] – q(x,y,z) = ρcp∂T(x,y,z)/∂t where ∇ is the Nabla operator, k(T) the thermal conductivity [W/(m-K)], q(x,y,z) is the heat density [W/m3], ρ is the density [kg/m3], and cp is the specific heat capacity [J/(kg-K)]. The real heat distribution is inhomogeneous, generating radial gradients that are far more critical than axial gradients for wave front deformation. The heat distribution used in the code takes into account both axial and transverse profiles. Axial variations are related to the absorption of pump light as it propagates through the crystal and reflects at the HR coated back surface of the active mirror. The transverse pump distribution in the gain medium is a circular supergaussian profile with intensity distribution I(x,y) ∞ exp(-[(x2 + y2)/wp2]N), where wp is the pump radius and N is the order of the supergaussian function. As mentioned previously, the heat load in the cladding is related to the absorbed fluorescence light and is estimated to be 45% of the pump energy. Figure 9 shows the transverse heat density distribution in the laser disk at axial position 0 (pump AR surface), L/2 (mid depth), and L (cooled HR surface). The disk and pump parameters are indicated in Table 1.
Fig. 9 Transverse heat density distribution resulting in the disk described in Fig. 8 when illuminated with a supergaussian circular pump distribution. Profiles are given for position 0 (red), L/2 (green), and L (blue).
Note that a discontinuity is observed at the Yb3+/Cr4+ doped interface, where strong spontaneous emission absorption takes place. Starting from that point, the heat density decreases exponentially towards the edges. The width of the Cr4+:YAG section is chosen to be large enough to prevent ASE-induced transverse oscillations to build along its diameter. We have calculated that considering a complete conversion of the pump energy into heat, the temperature rise within each pump pulse would be as low as 1.8 K. Considering the roughly 80 K temperature difference between the heat sink and the gain medium, the transient effects were neglected in a first approximation, i.e. ∇[k(T)∙∇T(x,y,z)] – q(x,y,z) = ρcp∂T(x,y,z)/∂t = 0.
4. Temperature distribution
The amplifier will be operated under vacuum to avoid any condensation on the AR surface. The pump AR-coated face of the disk will therefore be thermally insulated. In order to minimize transverse temperature gradients, it is convenient to insulate the disk peripheral surface. These boundary conditions were therefore considered in our model. Figure 10 shows the radial temperature profiles of the cryogenically-cooled Lucia amplifier (Fig. 8) at the pump (z = 0) and the cooled (z = L) surfaces for a helium layer thickness equal to 180 μm and a pressure of 2000 Pa.
Fig. 10 Radial temperature profiles of the cryogenic amplifier at the pumped (z = 0) and cooled (z = L) surfaces. A 180 μm thick helium cell at 2000 Pa pressure is considered. Radial coordinates below 1.72 cm (left of vertical dash line) define the extraction area, while larger values define the cladding peripheral area.
The maximum temperature is located in the center of the amplifier (left on the graph) with a value of 162 K. The radial thermal gradient within the extraction area (0 < r < 1.72 cm) is less than 1 K. The temperature difference between both curves also indicates that the axial gradient is about 10 K.
The impact of the helium gap thickness on the resulting temperature distribution was evaluated for thickness varying from 100 to 220 μm at a pressure of 2000 Pa (see Fig. 11 ). While the shape of the temperature profiles is similar for all gap thicknesses, the average temperature is changing over a wide range (from 136 K to 174 K, i.e. 0.3 K.µm−1). Note that the temperature gradients along the radial profile are very weak and do not exceed 4 K in the worst case (for a gap thickness of 220 µm).
Fig. 11 Axial(top) and radial(bottom) temperature profiles of the cryogenic amplifier for 100 μm, 140 μm, 180 μm, and 220 μm He gaps at 2000 Pa. In the top figure, the helium gap position is shown by the abrupt drop in temperature at 1.44 cm axial coordinate. Above this value, a constant 77K Cu temperature is observed.
The impact of the helium pressure on the resulting temperature distribution was also evaluated as illustrated on Fig. 12 , where the He pressure varied between 500 and 106 Pa (k bulk) for a fixed gap thickness of 100 µm. These curves illustrate again the strong temperature tuning capability offered by this technique.
Fig. 12 Axial (top) and radial (bottom) temperature profiles of the disk amplifier for 500 Pa, 900 Pa, 5000 Pa, and 106 Pa (k bulk) helium pressure. The gap thickness is fixed at 100 µm.
In the 500 – 5000 Pa domain, the temperature increases from 126 K to 195 K. This means that a pressure variation as small as 65 Pa implies a 1 K change in temperature, a tunability easy to achieve with standard pressure regulation devices. We also observe that helium gas pressures below 104 Pa are more favorable because the sensitivity to temperature is strongly decreasing above this value. This phenomenon is actually easily observable in Fig. 4, where the thermal conductivity dependence of helium with pressure saturates above 104 Pa.
The width and Cr4+ doping level of the YAG cladding located around the pumped Yb3+ doped central area are critical to achieve proper thermalization of the disk at the desired average temperature, while minimizing radial gradients. The average axial temperature dependence on helium gap thickness at 2000 Pa pressure is displayed for 1 and 2 cm cladding widths in Fig. 13 where we observe a significant impact illustrated for instance when comparing temperatures (174 K vs. 132 K) for the 100 µm gap thickness.
Fig. 13 Average axial temperature as a function of He gap at 2000 Pa for 1 and 2 cm cladding widths.
The figure also shows that in order to set the average temperature near the targeted 160 K, a helium gap thickness of 75 μm would be required for a 1 cm cladding (red line), whereas for the 2 cm cladding (blue line) a thickness of 190 μm is needed. Considering helium thermal conductivity dependence with pressure, we propose to build a finely tunable cooling system by setting the thickness at 100 µm with a 2 cm wide cladding periphery. Selecting the helium pressure between 500 Pa and 5000 Pa will allow an adjustment of the gain medium temperature between 195 K and 120 K.
5. Conclusions
We have demonstrated the benefits of sub-atmospheric pressure, sub-millimeter thickness helium gaps for cryogenically cooled active mirror laser amplifiers. This approach was illustrated in the context of LULI’s Lucia project, where the heat flux to be removed from the gain medium ranges between 1 and 10 W/cm2. The presence of a gas cell in contact with the HR face of an active mirror favorably impacts the lifetime of this dielectric layer. Alternative cooling solutions would involve solid materials like indium (commercial thin disk lasers) or liquids like H2O or LN2 (as for the current Lucia amplifier head or TRAM). Considering the high level of expected laser fluence (>10 J/cm2), operating the fragile HR coating in contact with a thin, static layer of an inert gas such as helium is a safer option. This is even more critical when considering Laser Induced Damage Threshold (LIDT) issues encountered by dielectric coatings at cryogenic temperatures.
Besides offering a safe solution for the gain medium’s long term integrity, the proposed approach provides a very flexible way of adjusting its average temperature. This capability is very advantageous when operating the laser at varying repetition rates, a flexibility often required by users.
This axial-only heat extraction scheme combined with a properly-designed (doping/width) Cr4+:YAG external layer and peripheral thermal insulation (vacuum) leads to a quasi constant transverse temperature distribution (<1 K) and a relatively small axial thermal gradient (<10 K). The gain medium is therefore operating in a regime far from thermal rupture because internal strains and stresses are negligible. Here again, long term reliability of the amplifier is positively impacted. The cooling concept presented here will be implemented in the second amplifier head on the Lucia laser at LULI.
Acknowledgments
The authors wish to thank J.-P. Périn, D. Chatain and F. Millet from CEA-SBT (Commissariat à l’Energie Atomique – Service des Basses Températures) for fruitful discussions while developing the described concept. The authors also gratefully acknowledge the support of the Délégation Générale à l’Armement of the Ministry of Defense of France and the MŠMT, Ministry of Education, Youth and Sports of the Czech Republic in supporting this work through the HiPER program.
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