Low Loss Sapphire Windows for High Power Microwave Transmission（二）
Summary of Results
The important objective of Phase II research was achieved: to fabricate and test a prototype high power sapphire microwave window. Unfortunately, high power testing of the window was not done as a result of parallel development of diamond windows elsewhere. Specific significant detailed results of Phase I are as follows:
Used epitaxial polishing techniques to strengthen set of sapphire windows.
Inspected polished disks to determine if they were adequately polished for strengthening.
Demonstrated that sapphire windows 0.5 mm thick with a 75 mm aperture could survive 5 atm pressure load.
Measured the strain and deflection of pressure tested windows.
Predicted the strain and deflection of pressure tested windows using modeling developed in the program.
Predicted maximum stress level in the thin windows using this modeling.
Failure tested windows of varying diameter, thickness, and polish were failure tested.
Failure tested windows with varying seal to aperture diameter ratios.
High temperature brazed a thin sapphire window into a metal fixture.
Fabricated a strengthened sapphire double window fixture in a realistic microwave apparatus.
Fabricated and tested a 75 mm diameter grid-cooled sapphire window under 1 kw heat load.
Fabricated and tested a grid-cooled sapphire window double window fixture in a realistic microwave apparatus.
Assembled and tested a microwave resonant ring for amplification and microwave response.
Tested a strengthened, sapphire double window fixture under 1 MW microwave power in a realistic microwave apparatus.
BACKGROUND
3.1. Introduction. There are a variety of materials available for use as a microwave window; ceramics are traditionally used because of their low losses and high strength [1],[2],[3]. The weaknesses of ceramics are their inherently statistical strength and their local impurities and defects that can result in power absorption and breakage caused by thermal stresses. Single crystal sapphire is now used because of its strength and high quality, but CVD diamond windows will be a major competitor in the future.
3.2. Properties of Sapphire. Sapphire is an unusual material because it is the hardest material and has the highest melting point of any material that is commonly available. Single crystal sapphire is widely used as a result of its transparency, its superior mechanical properties, its chemical and scratch resistance, and the fact that it can be relatively easily manufactured as a grown crystal. Crystals are grown in diameters up to 15 inches, but the process is expensive as a result of sophisticated control and long growth periods. Sapphire has special optical properties in that it has a large surface reflection and is optically active as well as birefringent. The basic sapphire reference is a book edited by Balyeav [4].
Mechanical Properties - Of all of the properties of sapphire, those related to its strength are the least well defined because the failure of sapphire is statistical. Mean properties cannot be used for design work; design values must be based on the minimum possible strength; tensile strength quoted as 410 MPa (design criterion) at 25°C. Minimum strength, however, is strongly dependent on manufacturing processes.
Mechanically, sapphire is currently characterized by the optical quality of the bulk single crystal, but there are no strict standards for describing the crystal, only approximate grades. The primary reason for this accepted imprecision is the lack of correlation of identifiable defects with macroscopic behavior, except for optical clarity. Optical grading is done both because large sapphire is usually used as an optical material, and because optical testing is the simplest and easiest technique used for identifying crystal defects. Properties that change significantly with crystal orientation are an important design criterion not encountered in most material design. One example is the maximum bending stress, which increases 50% from its lowest value as the direction of stress is changed. In many systems the piece axis is typically chosen to coincide with the crystal C-axis so that the properties of the piece are symmetric around the principal stress axis.
Single crystal sapphire typically fails by a fracture process that is very complicated, analogous to brittle (versus ductile) fracture in metals. The failure normally begins at a stressed surface imperfection where a crack begins to grow through combined chemical and mechanical effects. The crack then propagates by a sequence of mechanisms that result in a rapid and total failure of the piece. Overall strength measurements are a result of this process [5] and are a statistical value depending in detail on the surface and a number of other factors. The science of fracture mechanics of crystals is not well developed at this time, although some statistical predictions can be made of strength.
Optical Properties - Optically, sapphire is an excellent material. It has high internal transmittance from 150 nm to 6000 nm in wavelength - from the far UV to the middle infrared. Its high index of refraction at visible wavelengths (1.77 vs. 1.5 for quartz) causes large surface reflection losses if uncoated. It is also birefringent, with an index of refraction that depends on both the polarization and direction of the incident light.
Electrical Properties - Sapphire is an excellent insulator, even at high temperatures, with a volume resistivity of 1014 ohm-cm. It has a dielectric strength of 480,000 volt/cm, a dielectric constant at room temperature of 9.4 for an electric field perpendicular to crystal c-axis, and 11.5 for E parallel to c-axis. It has a very low loss factor, tan δ, of about 10-4.
Thermal Properties - Sapphire responds thermally in a manner quite similar to some steels. The thermal conductivity values of sapphire are closest to that of stainless steel, while its thermal diffusivity is closest to plain carbon steel. Sapphire maintains its structural integrity up to 1600-1700°C, when it becomes increasingly plastic, until it melts at approximately 2000°C. The thermal properties of sapphire at 25°C are: Thermal conductivity (60 ° to C-axis ) = 0.065 cal/cm-sec-°C, thermal expansion coefficient = 8.40 x 10-6 per °C (60 ° from C-axis, specific heat = 0.10 cal/gm; heat capacity = 18.6 cal/°C-mole.
Thermal Stress - Thermal stress, the generation of mechanical stress due to differential thermal expansion, is important both in the manufacture the use of sapphire. This is due to comparatively large coefficients of both thermal conductivity and thermal expansion, together with anisotropic crystal properties. Residual thermal stress prevented the manufacture of large sapphire crystals until the 1940's [4]. The overall thermal stress is determined by the total temperature difference across the crystal. The controlling property is the thermal diffusivity, α = k/ρ c where k is the thermal conductivity, ρ, the density, and c, the specific heat.
3.3. Sapphire Processing. Sapphire of a desired shape is cut from grown boule by diamond saws, then final machined and polished. Polishing sapphire is very difficult because it is so hard, but good polishing techniques are available [6]. Sapphire is the third hardest material known, following diamond and cubic zirconium, with a MOH rating of 9. A standard 60/40 optical glass polish does not describe non-flat sapphire windows because sapphire can only be machined flat on a microscale for flat windows. Other shapes such as cylinders are precision machined and the undulating surface is then polished. The best sapphire polish available is an "epi-finish" that is supposedly an epitaxial surface. In this process, all of the scratches are removed by diamond dust polishing followed by a final chemical polish.
Sapphire Strengthening Research. Since the strength of a high quality piece of sapphire is determined by the condition of its surface, the preparation of that surface is crucial in an application demanding maximum strength. The process of strengthening sapphire by modifying its surface has long been known and practiced in the form of fire polishing. Fire polishing heals surface flaws but can only be used for small pieces as a result of the large thermal stresses it creates in large pieces. More recently standard optical polishing techniques have had some success in strengthening sapphire. [7]
For surface strengthening to be effective the unprocessed condition of the surface must be the determining factor for the macroscopic strength of the single crystal sapphire, and not any bulk flaws. The surface quality is most important at locations where there are large, local tensile or shear stresses are present. The surface condition at the position of maximum stress may not be relevant, however, because some other location on the surface may have half the stress but be unpolished (typically the edge of the piece). Stress distribution is determined by both mechanical and thermal loading, as well as any residual stresses in the piece itself.
The obvious techniques for removing surface flaws such as mechanical or chemical polishing have been unreliable for strengthening sapphire in the past. Improvements in the strength of sapphire have been demonstrated using: 1) Polishing, 2) Healing of surface flaws (chemically or through high temperatures), 3) Protecting the surface 4) Sealing surface flaws (solid solution layers), 5) Compressive surface layers, and 6) Crack propagation prevention (dislocation pinning). The research problem has been to discover which mechanisms are most effective for strengthening sapphire, and to find a practical technique that successfully performs the appropriate change at the surface of an arbitrarily shaped piece of sapphire. Unfortunately, practical experimental strengthening techniques almost always improve the surface through a number of the above mechanisms simultaneously. Kirchner [8] obtained compressive surface layers on a variety of ceramic materials; treatment of sapphire single crystals resulted in three-fold improvements in strength. Compressive surface stresses cause much larger tensile stresses to be required for crack growth and propagation.
An important issue associated with surface strengthening is surface protection. The environment effects the strength of sapphire through chemical enhancement of crack propagation and handling or mounting damage. Although sapphire is very hard and very scratch resistant, it is easy to microscopically scratch an unprotected surface because of the omnipresence of hard particles in the form of alumina on "sand" paper, as well as chips from the edges of the sapphire piece itself.
3.4. Microwave/RF Window Design. The discussion given below is appropriate to both microwave and radio wave (RF) transmitting windows, the only difference being the wavelength of the radiation and the dependence of the absorbencies and reflectivity on the wavelength. In the case of microwave and millimeter-wave radiation, the gyrotron is the primary means for generating high power, and it is based on cyclotron resonance coupling between microwave electric fields and electrons in vacuum. A gyrotron can produce very large amounts of pulsed (GW) or CW (MW) power output at wavelengths in the millimeter range. [9],[10] One of the important design problems in scaling gyrotrons to higher power levels or shorter wavelengths is transmitting the output power through a window in the vacuum envelope. Traditionally, polycrystalline ceramics such as alumina and BeO have been used as window materials, but sapphire (single crystal alumina - α -Al2O3) has also been used. The trend toward shorter wavelengths (higher frequencies) may make other materials more appropriate for windows. New methods of fabrication which allow higher purity or greater strength are increasing the capabilities of other materials such as Si3N4, AlN, and especially diamond.
A gyrotron operated in a CW mode places stringent constraints on window materials and design because the microwave losses in the window material result in significant temperature gradients, and only moderate gradients produce stresses that will break the window. The waveguide mode of interest for millimeter wave gyrotrons and waveguide systems is gaussian-like HE11 mode as a result of its low-loss propagation and pure linear-polarization in corrugated waveguide. The latest gyrotron designs are utilizing "flattened" electric field profiles at the output window by using mode mixtures (HE11 + higher modes) to reduce the peaking of the central power deposition which occurs in the HE11 mode. A typical current CW gyrotron window design uses two discs of ceramic placed with their axes parallel with the cylindrical waveguide. The two discs are separated by a carefully controlled amount to form a channel for coolant between the discs and to achieve resonant transmission of the microwaves through the disks. This configuration provides face cooling, which minimizes the length of the path for heat conduction through the ceramic so that the window thermal conductivity is not of major importance.
A number of desired properties for window materials can be derived from the details of their application to Fusion plasmas heating. The ceramics and the coolant should have minimum microwave loss - (ε ′)1/2tanΔ - where ε ′ is the dielectric constant in the material, and tanΔ is the loss factor. The mechanical strength should be as high as possible in order to withstand 1) the pressure forces created by the vacuum on one side and the coolant pressure on the other, and 2) the thermal stresses induced by uneven heating. The window must be an integral and perfectly vacuum tight part of the vacuum envelope. A braze joint involving a temperature cycle of the order of 800 to 1000°C is desirable. The window material must have a low vapor pressure at operating temperature (< 10-9 torr at 100°C for example), and be resistant to deterioration of any of these parameters under significant neutron radiation doses. Because the mechanical stresses which can break the window are increased significantly by temperature variations, material parameters such as Young's modulus and the coefficient of thermal expansion should be as small as possible.
Typical gyrotrons use oversized output waveguides. The guide diameter can be on the order of 6.5 to 9.0 cm, which may be equivalent to 6 to 30 free space wavelengths, depending on the operating wavelength. The window disc diameter may be 2 to 5 cm larger than the guide diameter. For proper microwave transmission each disc should be approximately an integral number of half-wavelengths thick. For mechanical purposes the disc thickness is typically about 0.25 cm. This can be one half of a wavelength (measured in the ceramic) or as many as three wavelengths, depending on the value of ε ′ and the operating wavelength.
A low value of ε ′ is desirable both because power loss is proportional to (ε ′ )1/2 and because a larger ε ′ results in a window which has a narrow frequency bandwidth. Although a gyrotron is nominally a single frequency device, a narrow window bandwidth makes it more difficult to keep the gyrotron oscillation within the desired frequency range as the gyrotron parameters such as beam voltage and current are varied of change with age. The purity of window material is also important. Inclusions can result in local hot spots, and additives that aid in forming the ceramic can increase losses even if they are uniformly dispersed. Surface cracks can result in significantly shorter window life. [11]
In the context of these parameters, sapphire is among the best materials available except for its relatively large coefficient of thermal expansion and thus thermal stress susceptibility. Commercial sapphire has a loss factor close to 10-4, small amounts of impurities, and high strength. Its dielectric properties have been studied in detail (e.g. [12]), and, its losses drop dramatically at cryogenic temperatures [12]. Finally it has the advantage of a low susceptibility to radiation damage [3], an important issue for long term use on reactors.
The desirable properties for the window cooling material include good heat transfer, such as high boiling point and heat capacity and low viscosity. Low ε ′ and microwave loss are useful but not as important as the heat transfer properties. Coolants that have proven useful include FC-75 (a fluorocarbon product of 3M Corp.) and tetradecane.
