Design and Analysis of High Power RF Window

Abstract

Gyrotron has proven to be an efficient source for RF generation at high power and high frequency level. Gyrotron has very significant and specific role to play, particularly, in plasma, material, spectroscopy and energy research. The chapter covers the selection of dielectric materials and power handling capability of RF windows. The design analysis of RF window with window disk thickness and diameter are optimized considering the minimum return loss and the minimum insertion loss by using CST microwave studio. The advantage of the double disc window cooling is most effective. In the 42 GHz window design, double disc winnow are using and the temperature on the disc of RF window does not exceed 100 degree C and found in safe limit. The design of RF window depends on the dielectric characteristics like dielectric constant, loss tangent, permittivity, etc., of the window materials. The dielectric permittivity and loss tangent of window material affect the absorption and transmission of RF power. The thermal analyses are performed by using finite element analysis code ANSYS code on the basis of electrical design of RF window.

1. Introduction

At present the Gyrotron is used almost in every plasma fusion machines as a high power millimeter wave source for electron cyclotron resonance heating (ECRH). RF window is a very critical component of a high power Gyrotron and used on the output section of the device for the extraction of RF power from vacuum to external pressurized atmospheric environment [1, 2, 3, 4, 5].

In high power microwave devices, RF window is also a critical component and used for extraction of RF power from the Gyrotron. RF window is used on the output section of the device for the propagation of RF power from the ultrahigh vacuum environment to the external normal pressure environment for the effective extraction of RF power. Thus the careful design of this component is essential for the successful operation of the device. The window disc dimensions are optimized in the design of a RF window taking into account the minimum power reflection and the maximum power handling capability.

RF loss in the RF window directly depends on the dielectric properties of the materials. Obviously, the dielectric properties should be stable in a wide range of temperatures so that the window performance remains stable during the heating. RF window must be fabricated from a low loss material which should be also suitable for the ultra-high vacuum application. Thus, the loss tangent of the RF window material should be minimum for the least absorption of RF power.

The material selection is very important for a Gyrotron window operating at high power and high frequencies. For a high power Gyrotron the advanced materials such as sapphire, chemical vapor deposited (CVD) diamond, silicon nitride composite, BeO, Au-doped silicon etc., have to be used [6, 7, 8, 9]. CVD diamond is the first choice for the MW power Gyrotron due to its excellent dielectric and mechanical properties.

The electrical and thermal designs of the RF windows for 42 GHz Gyrotrons are presented in this Chapter. It is of interest to mention that gyrotrons operating at these two frequencies are considered for study as both of these gyrotrons have been developments at CEERI, Pilani under various national projects. The various types of RF windows used in a Gyrotron are discussed in Section 2. The electrical and thermal designs of RF window for 42 GHz Gyrotron is described in Section 3.

2. Gyrotron RF window

Gyrotron window is required for transmitting significant amount of microwave energy without exhibiting thermal runway. The design requirement of RF windows is minimum return loss, minimum insertion loss, power handling capacity and broad bandwidth. Different dielectric material such as, boron nitride, silicon nitride, sapphire and PACVD diamond are used in a design of RF window. Commonly, boron nitride, silicon nitride and sapphire are used in low power and short pulse Gyrotron window. The combination of low millimeter wave losses and excellent thermal conductivity with good mechanical properties makes artificial plasma assisted chemical vapor deposition (PACVD) diamond a compelling choice for high power, high frequency long pulse Gyrotron window. The diamond window gives a solution for the window problem which has been regarded as the most serious issue on the development of high power long pulse Gyrotron [10, 11, 12, 13, 14, 15, 16].

In double disc window, two discs are required per barrier with a spacing of approximately one wave length and some power is absorbed by dielectric cooling liquid, which are disadvantages of this types of window. Due to moderate RF power double discs sapphire window has been selected for use in 42 GHz, 200 kW Gyrotron and presented in Section 3. In single disc window, low loss tangent dielectric materials such as boron nitride, silicon nitride, sapphire and plasma assisted chemical vapor deposition (PACVD) diamond are used. The disc is built into an assembly in which two Inconel tubes are bonded on both sides of the plate to provide vacuum shielding and water cooling to the edge of the disc, leaving an effective window aperture of 85 mm. The PACVD diamond window can be used for 1 MW Gyrotron due to its high thermal conductivity and low dielectric loss. Diamond grown by chemical vapor deposition (CVD) is becoming a viable window material [17]. Window must be able to withstand the thermally induced stresses caused by the temperature rise of the window as well as the mechanical stress caused by atmospheric and coolant pressure [18]. In the Gyrotron, different types of windows according to the various cooling schemes are used for the extraction of RF power. Generally, windows with (a) multiple dielectrics with distributed cooling (b) double discs with surface cooling by liquid (c) single disc with surface cooling by gas and (d) single disc with edge cooling are used in Gyrotrons. Each of these windows possesses its own advantages and disadvantages. Basic aspects of gyrotron window are discussed in sub-Section 2.1. Further, the selection of dielectric materials for Gyrotron window is presented in sub-Section 2.2 and the power handling capability of RF window in sub-section Section 2.3, respectively.

2.1 Basic aspect

Ultimately, the high power limits for all RF window is a result of heating caused by absorbed microwave energy in the window. Even though the fraction of energy absorbed is quite small, of the order of 0.1% for typical materials of interest, the large amounts of transmitted power means that even a small fraction can result in significant heating leading to thermal stress and thermal runaway. In the heated RF window structure thermal energy generation is initiated by the absorbed microwave energy [19]. This energy is removed in steady state operation by thermal conduction and force convection. The conduction temperature profile is important because it ultimately leads to failure of the window when the power is high. The temperature gradients required to drive thermal energy out of the window cause different areas of the window. As window heat up, these stresses would reach the ultimate strength for the given material and surface of geometry and the window would fail. Face cooled window is not as susceptible to thermal runaway effects as edge cooled window.

The thickness (d) of window disc is chosen so that the reflection is minimized and it may be initially estimated through the expression given as [20]

$$d=\frac{N{\lambda }_0}{2\sqrt{{\epsilon }_r^{\prime }}}$$E1

where N is integer and ${\lambda }_0$ is the free-space wavelength, the maximum transmission occurs at the series of frequencies f_i for which

$$N_i{\lambda }_i=2d\sqrt{{\epsilon }_r^{\prime }}$$E2

where suffix i signifies the various integers. A possible solution for broadband window is Brewster window. Brewster window is used in multi frequency Gyrotron. Window reflections are the main problem in the design of Brewster window. The transmission band of Brewster window is large and the disk in the window is tilted with a specific angle. The angle between the normal to the window disk and the RF propagation axis is chosen according to Eq. (3).

$${\theta }_{\mathit{\text{Brewster}}}=\mathit{arc}\mathit{tan}\sqrt{{\epsilon }_r^{\prime }}$$E3

The value of disc thickness ($d^{\prime }$) in case of TE_mn mode for low power window can be obtained as:

$$d^{\prime }=\frac{\mathit{N\pi }}{\sqrt{{\left(2\mathit{\pi f}\sqrt{\frac{{\epsilon }_r^{\prime }}{c}}\right)}^2-{\left(\frac{{\chi }_{\mathit{mn}}^{\prime }}{R_{\mathit{win}}}\right)}^2}}$$E4

where f is frequency, R_win is window radius, c is velocity of light and ${\chi }_{\mathit{mn}}^{\prime }$ is the n^th root of the derivative of m^th order first kind Bessel function. Based on this formulation the range of disc and other design parameters considered. It is interest to mention that Eq. (4) can be easily transformed as Eq. (1) for gyrotron window due to insignificant value of second term of the denominator of Eq. (4). The initial disc thicknesses (d) of high frequency window, obtained from eq. (1), for various high power Gyrotrons are given in the Table 1.

Materials	At 120 GHz $d=\frac{4{\lambda }_0}{2\sqrt{{\epsilon }_r^{\prime }}}$	At 170 GHz $d=\frac{5{\lambda }_0}{2\sqrt{{\epsilon }_r^{\prime }}}$	Permittivity (${\epsilon }_r^{\prime }$)
Boron Nitrate (BN)	2.3 mm	2.03 mm	4.7
CVD	2.1 mm	1.85 mm	5.67
Sapphire	1.63 mm	1.44 mm	9.4

Table 1.

Disc thickness for different frequency Gyrotron window.

The effect of varying the window radius is illustrated in Figure 1. With the larger window the power handling capacity increases. However, as increase in the window thickness raises the total heat generated in the window and thereby is detrimental to the window thermal performance. It shows that the maximum acceptable power level decreases when the window thickness is increased.

Figure 1.

Effect of window radius on maximum power level of window.

2.2 Selection of window materials

The important aspect of high power Gyrotron window design is the dielectric properties of the window materials. Since the ceramic comes in the path of propagating microwave, the dielectric properties of the ceramic material have strong influence on the electrical design of window. Desired dielectric properties of a window material are low relative permittivity (${\epsilon }_r^{\prime }$) and low loss tangent (tan δ). If all else have been optimized, a lower relative permittivity (${\epsilon }_r^{\prime }$) gives a better bandwidth response [21].

Alumina is the predominant material for high power window applications. Beryllia, though better in electrical and thermal properties than alumina, is seldom used. Beryllia is not mechanically strong, and the potential danger in handling such a toxic material is also a definite drawback. Sapphire has been the best material for a microwave window because of its high strength, low absorbed power and good tolerance of radiation damage. Sapphire is a single crystal material because it is hardest material and has highest melting point of any materials that is commonly available in the industry. Sapphire materials are widely used because its transparency, superior mechanical strength, chemical and scratch resistance and the fact that it can be relatively easily developed as a grown crystal. Sapphire also has the potential for much lower microwave losses as a result of its large reduction in loss tangent at cryogenic temperatures, where it also becomes somewhat stronger.

The effect of poor thermal conductivity was identifiable from the extremely high temperature gradients (up to 600°C) attained immediately prior to failure, but they can handle up to 100 kW power. The dielectric properties should be stable in wide range of temperature so that the window performance being stable during the heating. Due to the very good thermal conductivity and very weak dependency of the dielectric parameters on temperature, diamond is selected for window design for high power and high frequency Gyrotron which is capable for long pulse operation. The diamond window gives a solution for the window problem which has been regarded as the most serious issue on the development of high power long pulse Gyrotron. For the low power Gyrotron the best materials like sapphire and boron nitride are used due to the low cost and easy availability.

The strength and thermal conductivity of PACVD has made it the leading candidate to replace sapphire in RF window applications. The edge cooled window is a major advantage of avoiding complex flow passages in the microwave channel. High power limit for all vacuum windows is a result of heating caused by absorbed microwave energy in the window elements themselves. Even though the fraction of energy absorbed is quite small, on the order of 0.1% for typical materials of interest, the large amounts of transmitted power means that even a small fraction can result in significant heating leading to coolant boiling, thermal stress failure, or thermal runaway. The small but significant absorption is due to a complex component of the dielectric constant, indicating that some polarized or charged constituents of the material move in phase with the applied electric field at the frequency of the microwave beam.

Dielectric materials such as sapphire and boron nitride (BN) are used in RF window for low power gyrotron due to its low failure resistance and low RF power capacity of material, while PACVD diamond is used in high power and long pulse gyrotron due to its high failure resistance and high power capacity of material. The expressions of these two empirical parameters, namely failure resistance (R’) and power transmission capacity (P_T) for edge cooled windows [20]. These parameters are defined as follows:

$$R^{\prime }=\frac{k{\sigma }_B\left(1-\upsilon \right)}{\mathit{E\alpha }}$$E5

where k is thermal conductivity, σ_B is bending strength, $\nu$ is Poissons number, E is Young’s modulus and α is thermal expansion coefficient. Further

$$P_T=\frac{R^{\prime }\rho c_p}{\left(1+{\epsilon }_r^{\prime }\right)\mathit{\text{tanδ}}}$$E6

where ρ is density, c_p is specific heat.

Using the material parameters and beam profiles, irradiation tests with a potential new material for simple water-edge-cooled single disc window, diamond is attractive due to its good mechanical properties, modest dielectric constant, relatively low loss and excellent thermal conductivity. In the temperature range of 200–370 K the loss tangent and the permittivity of diamond are practically constant. The current CVD capabilities have allowed for tests with diamond discs of up to 100 mm diameter and 2.5 mm thickness for megawatt Gyrotrons.

2.3 Power handling capability

RF windows are generally preferred and used for high power microwave tubes due to their higher handling RF power capacity. Performances of microwave tubes are limited by a number of factors; these are heat dissipation, voltage breakdown, and window failure and multipactor phenomena. The maximum power obtainable from a microwave tube is often determined by the power handling capability of the output window. The output RF power is propagated out through waveguide or coaxial line windows. The power handling criteria is rather a check for the diameter and indirectly sets a limit to the useful diameter.

The power profile in the output window can take a variety of shapes. The most desirable profile is Gaussian distribution which simplifies coupling of the RF into a waveguide for transport to the plasma. The failure of RF windows may happen in high power microwave tubes due to the following two reasons. (i) The ceramic disc in window is bombarded by high energy electrons or ions and gives rise to multipactor phenomena that causes discharge on the surface of the ceramic disc. As a result, the ceramic disc is perforated or cracked. And, (ii) The heat losses generates excessive heat in the ceramic disc and the temperature profile of the ceramic disc rises up too high that it cracks developed because the tension caused by excessive heat expansion is too strong to be endured by the material. The most intractable problem for a window used to transmit high power continues wave (CW) results from the excessive heat generated by RF losses in the dielectric disc. Although there are several causes that may generate heat in dielectric disc, the above-mentioned two kinds, that is, electron bombardment and RF losses are the most dominating heat sources in the dielectric disc in a window used to transmit high power CW, and they must be taken into account seriously. Cylindrical TE mode window is comprehensively used in high power microwave tubes. It consists of a thin dielectric disc. When microwave passes through the dielectric disc, charge polarization would be induced and thus yielding RF loss causes the thermal heat in the window material. Because the heat dispersed from the interface of the disc with vacuum or air is too little to be considered, it is transmitted only by conduction to the edge and dispersed through metal window frame and cooling fluid, thus a thermal equilibrium is reached. The edge of the dielectric disc keeps on constant temperature under well cooling condition. The temperature in the centre of dielectric disc is the highest when the thermal equilibrium is reached. If the temperature difference between the center and the edge surpasses a certain limit, the dielectric disc may crack. Assuming the temperature difference between the centre and the edge of the dielectric disc to be T_m, then one can write:

$$T_m=0.725\frac{f{\epsilon }_0{\epsilon }_r^{\prime \prime }{P}_0{Z}_d}{h}$$E7

where h is the heat conductivity coefficient, f is frequency, $P_0$ is passing power, ${\epsilon }_0$ is permittivity in the free space medium, ${\epsilon }_r^{\prime \prime }$ is loss factor in the dielectric medium and Z_d is the characteristic impedance of TE_0,3 mode in dielectric disc and expressed as follows:

$$Z_d=\frac{\sqrt{{\mu }_0/\left({\epsilon }_0{\epsilon }_r^{\prime }\right)}}{\sqrt{1-{\left(\frac{{\lambda }_0}{{\lambda }_{c03}}\right)}^2}}$$E8

where ${\mu }_0$ is permeability in free space medium, ${\lambda }_0$ is free space wavelength and ${\lambda }_c$ is cutoff wavelength. Therefore, a formula of average power capacity $\left(P_{\mathit{\text{Total}}}\right)$ of cylindrical TE_mn mode window can be acquired as follows:

$$P_{\mathit{\text{Total}}}=8.67\frac{h∆T_m}{\omega {\epsilon }_0{\epsilon }_r^{\prime \prime }{Z}_d}$$E9

where $∆T_m$ is the endurable maximal temperature difference between the centre and the edge of a dielectric disc. The temperature increment should be as large as possible to be endured by ceramic disc. Moreover, it has been concluded in that the maximal endurable temperature difference between the centre and the edge of dielectric disc made of ceramic is about 100 K.

1. RF Power loss in waveguide: For TE cylindrical waveguide mode profile function f (z) = $e^{-{\mathit{ik}}_{z}z}$ of a forward propagating wave, the power flow in the waveguide is given by:

   $${\mathrm{P}}_{\mathrm{rf}}=\frac{1}{2{\mathrm{\mu }}_0}\int \left|\mathrm{E}\times {\mathrm{B}}^{\ast }\right|\mathrm{da}=\frac{\pi k_z}{4{\mu }_0\omega k_{\perp }^2}\left({\chi }_{\mathit{mn}}^{{\prime }^2}-{P_0}^2\right)J_m^2\left({\chi }_{\mathit{mn}}^{\prime }\right)E_0^2$$E10

   where E and B^* are the electric and the complex conjugate of magnetic field respectively, E₀ is amplitude of electric field, $P_0$ is passing power and $k_z$, $k_{\perp }$ are the axial wave number and the transverse wave numbers, respectively. Further, the ratio of ohmic loss to RF loss in the window is given by

   $$\frac{{\mathrm{\rho }}_{\mathrm{ohm}}}{{\mathrm{P}}_{\mathrm{rf}}}=\sqrt{\frac{2}{{\mathrm{\mu }}_0\mathrm{\omega \sigma }}}\frac{{\mathrm{k}}_{\perp }^4}{\mathrm{\pi }{\mathrm{k}}_{\mathrm{z}}}\frac{1}{\left({\mathrm{\chi }}_{\mathrm{mn}}^{{\prime }^2}-{{\mathrm{P}}_0}^2\right)}\left(1+\frac{{\mathrm{m}}^2{\mathrm{k}}_{\mathrm{z}}^2}{{\mathrm{\chi }}_{\mathrm{mn}}^{{\prime }^2}{\mathrm{k}}_{\perp }^2}\right)$$E11

   TE_0nmode: The RF power generated in a TE_mn circular waveguide mode and incident on a window disc of radius (R) can be found by using Poynting theorem. For azimuthally symmetric modes with m = 0, we found power density distribution, S_z (r) as

   $$S_z\left(r\right)=\frac{P_{\mathit{\text{Total}}}{\chi }_{\mathit{mn}}^{{\prime }^2}}{\pi R^2}\left[\frac{J_1^2\left(\frac{{\chi }_{0\mathit{nr}}}{R}\right)}{J_0^2\left({\chi }_{0n}\right)}\right]$$E12

   where $P_{\mathit{\text{Total}}}$ is the total power.

   TEM₀₀Gaussian beam mode: For a fundamental symmetric Gaussian beam, the power density distribution is given by

   $$S_z\left(r\right)=P_{\mathit{\text{Total}}}\frac{2}{\pi w^2}{e}^{-2{\left(\frac{r}{w}\right)}^2}$$E13

   where w is the Gaussian beam radius, defined as the value of r at which the field amplitude is 1/e times its on axis value. Thus the radial power absorption in the disc can be modeled by:

   $$P\left(r\right)=A{S}_z\left(r\right)$$E14

   where A is the power absorption coefficient and is given as:

   $$\mathrm{A}=2\mathrm{\alpha }\mathrm{l}$$E15

   where α is the attenuation due to a dielectric region of length l in a waveguide.

2. RF loss in ceramic window: The RF loss in the ceramic window may be written as

   $${\alpha }_0=\frac{2\mathit{\pi f}}{c}\sqrt{{\epsilon }_r^{\prime }}\mathit{\text{tanδ}}S$$E16

   where ${\alpha }_0$ is the absorption loss. Further, S is the enhancement factor in the absorption due to the fact that the windows are acting as Fabry-Perot. S is close to unity when the window is made anti-resonant (which requires a tolerance on the window thickness). For the case of resonant power transmission, which is considered here, S is given as:

   $$S=\frac{\left(1+{\epsilon }_r^{\prime }\right)}{2\sqrt{{\epsilon }_r^{\prime }}}$$E17

   On the basis of eq. (10)–(17), an algorithm has been found out and computer program in MATLAB has been developed. Figure 2 shows the power distribution S_z(r) and loss on the disc for TE mode.

   Table 2 gives the enhancement factors and RF losses in the ceramics for different dielectric materials. Table 3 gives the power density distribution in the edges of the sapphire disc, calculated. In the same way, Table 4 gives the power handling capacity of sapphire window for 42 GHz Gyrotron at high temperature estimated.

Figure 2.

Power distribution S_z(r) vs. disc of radius for TE mode.

Materials	Enhancement factor (S)	RF losses in ceramic (α0) At 42 GHz	RF losses in ceramic (α0) At 120 GHz
Sapphire	1.7	0.90	2.61
CVD	1.4	0.05	0.16
BN	1.3	2.83	8.10
Alumina	1.7	0.46	1.31

Table 2.

RF losses in the dielectric for different materials.

S.No.	Input parameters	Value	Power distribution in edges of disc Sz(r)
1.	Output power (P0)	200 kW	78 kW
2.	Mode (TE mn)	TE0,3
3.	Waveguide Radius (a)	42.5 mm
4.	Frequency (f)	42 GHz

Table 3.

RF power distribution in the sapphire disc window.

Input parameters	Value	Power handling capacity (PT)	Remarks
Radius (a)	42.5 mm	194 KW	(ΔTm) Temperature difference is high power capacity (PT) will be increased.
Passing Power (P0)	200 kW
Frequency (f)	42 GHz
Temperature difference $(∆T_m$)	107 K
Characteristic impedance of TE0,3 mode (Zd)	135 ohm

Table 4.

Power handling capacity (P_T) of sapphire window.

3. Design of RF window for 42 GHz, 200 kW Gyrotron

The design of face cooled double discs window for 42 GHz, 200 kW Gyrotron has been carried out using the CST microwave studio (CST-MS). The window disc thickness and diameter are optimized considering the minimum return loss and the minimum insertion loss. The dielectric properties are used for the S-parameter estimation in CST simulation and the mechanical and thermal properties are used for the thermal and structural analysis of RF window in ANSYS simulation. In this section, the electrical design of RF window for 42 GHz, 200 kW.

3.1 Electrical design of RF window for 42 GHz Gyrotron

In 42 GHz, 200 kW Gyrotron double discs, each of diameter 85 mm and thickness 3.2 mm sapphire window and spacing of discs 2.7 mm have been optimized in the simulation where sapphire discs are face cooled by Coolant FC-75. These values of window disc diameter, thickness and spacing are optimized considering the minimum return loss (≤ − 20 dB) and the minimum insertion loss (≤ 0.1 dB) by using CST microwave studio [22]. Figure 3 shows the schematic diagram of double disc faced cooled sapphire window for 42 GHz Gyrotron. The material of disc is sapphire and dielectric constant (${\epsilon }_r^{\prime }$) of the sapphire is 9.41, loss tangent is 5.4 × 10⁻⁵ while dielectric constant of FC-75 is 1.8 and loss tangent (tan δ) is 26 × 10⁻⁴.

Figure 3.

Faced cooled double disc window for 42 GHz Gyrotron.

The design flow chart of high frequency and high power Gyrotron window is shown in Figure 4. The performance of the S-parameters for 42 GHz double discs faced cooled window with respect to frequency is shown in Figure 5. The S parameter simulations for the optimized RF window show very small reflection and absorption in the RF power. The disc thickness of window is small shows some advantages such as proper metallization for better mechanical strength and brazing. The reflection and transmission of the window are independent from the diameter as the wavelength is quite small as compared to the ceramic disc outer diameter. The return loss performance with respect to frequency for various RF window disc thicknesses of sapphire material is shown in Figure 6.

Figure 4.

Design flow chart for any Gyrotron window.

Figure 5.

Return loss performance of double disc sapphire window for 42 GHz Gyrotron.

Figure 6.

Return loss performance of different thickness for sapphire disc window.

3.2 Thermal design

On the basis of electrical design of RF window, the thermal and structural analysis are performed by using finite element analysis code ANSYS [23]. The objective of thermal analysis is to assess the temperature distribution, axial stress, radial stress and thermal expansions in the RF window for the 42 GHz Gyrotron during extreme case of operation, that is, at saturation. The return loss and insertion loss of the RF window have been obtained as −49.5 dB and − 0.02 dB, respectively. Using these values of return loss and insertion loss, the reflected, transmitted and the absorbed powers by double sapphire discs can be easily estimated as 0.001%, 99.54% and 0.42%, respectively. The beam-wave interaction simulation results carried out in Gyrotron Lab, CEERI, shows 280 kW RF power generation in the interaction cavity and thus 1176 W RF power is absorbed by the window disc in double discs sapphire window. This absorbed power is distributed all over the disc surface as TE₀₃ mode.

A transient thermal analysis is used to determine the temperature distribution as a function of time. The input parameters are heat flux, film coefficient and bulk temperature are using in the analysis. The output parameter is the temperature distributions on RF window. The design of cooling system is chosen so that maximum surface of the window is covered and flow rate of coolant is varying and optimized from 5.0 to 10 lit/min for maximum cooling. The windows boundaries consist of two parallel faces with coolant in between and heat flow across the other face is given as:

$$q=h\left(T_s-T_b\right)$$E18

where h is heat film coefficient, $T_s$ the surface temperature of the disc and $T_b$ bulk temperature of the coolant. The edges of the sapphire disc are assumed to be isolated. The heat flux is given as an input parameter in the thermal simulations. First of all, the heat film coefficient is optimized considering the effective cooling of the window disc. The window geometries are optimized for the effective cooling. Normal water (288 K) is used as a coolant in the thermal simulations of the double discs sapphire window. Temperatures on centre of disc and edge of the disc in double discs window geometry are 77.13°C and 35°C, respectively.

4. Conclusion

The design methodology of RF window for high frequency Gyrotron is presented in this Chapter. Both electrical and thermal analysis for microwave window design has been discussed in this Chapter. At first, the various basic aspects, the selection of window materials and the power handling capability of high power window have been discussed. It is found that Sapphire and BN can be used in moderate power Gyrotron but CVD diamond is must for megawatt gyrotron. In 42 GHz, 200 kW Gyrotron double discs, each of diameter 85 mm and thickness 3.2 mm sapphire window and coolant FC-75 has been optimized in the design using CST microwave studio. In the presented thermal design through ANSYS simulation, the temperature on the disc of RF window does not exceed 100°C and thus within the safe limit. The subsequent thermal stresses also do not deteriorate it. Single disc edge cooled window geometry is used for Gyrotron tube which allows the microwave radiation to exit the tube. The thermal analyses are performed by using finite element analysis code ANSYS code on the basis of electrical design of RF window. The temperature on centre of disc and edge of the disc in single disc window geometry are found as 376 K and 310 K, respectively. The water-edge-cooled CVD diamond window provides a practical technical solution for the transmission of continuous millimeter wave transmission in excess of 1.0 MW.