Design of C Band High Power Teflon Water Load

A C band Teflon water load is designed for the 4.6 GHz lower hybrid current drive (LHCD) system in the experimental advanced superconducting tokamak (EAST) to absorb the high power microwave reflected from the circulator, Teflon is used to substitute traditional ceramics to isolate the air and the water, which is cheaper and easier to processed. The simulation result carried out by CST microwave studio shows that the return loss reaches -64 dB at 4.6 GHz, and the power loss density was fitted by Origin software to calculate the thermal distribution of the Teflon and the water. Besides, the thermal analysis carried out by ANSYS indicates that this water load can work under 5 kW CW, with the maximum temperature of Teflon less than 71 °C, and the maximum thermal deformation and stress are no more than 0.14 mm and 3.2 MPa.


Introduction
Water load can be used to absorb high power microwave generated by many different high power microwave sources such as klystrons [1][2][3], magnetrons [4], gyrotrons [5][6][7], accelerator [8] and some other devices [9][10][11]. Traditional water loads used to adopt special ceramics, alumina (Al2O3), beryllium oxide (BeO) and aluminum nitride (AlN), to isolate the air and the water or keep the vacuum environment. Compared to these ceramics, Teflon has the similarly excellent microwave performance with low loss tangent (at 25℃). Besides, Teflon is a mature plastic material which is easy to produce and process, its price is only nearly 10 percent of alumina's price and less than 1 percent of beryllium's or aluminum nitride's price, which shows potential value in microwave engineering. While the coefficient of thermal conductivity and the melting point of Teflon are only 0.25 W/m and 327 ℃, respectively. As a result, it can just work under several kilowatts steady state or at megawatt level for several microseconds.   Fig.1, in the 4.6 GHz 250kW LHCD system of EAST, each transmission line has 2 water loads connected with the circulator to protect the klystron from the high power reflecting microwave. In the port 3 of the circulator, this water load must have the ability to absorb more than 99 percent reflecting energy, and the rest of the energy (less than 2.5 kW) can be absorbed by water load at port 4. Above all, Teflon water load would be a more affordable structure to be adopted at port 4. In section II, this work aim to calculate the physical size and the simulate the return loss, power loss density by CST microwave studio. In section III, the power loss density was fitted by Origin to analysis the thermal distribution in the Teflon and the water with * functions. Section IV indicates the thermal analysis results carried out by ANSYS Fluent, which show that the Teflon water load can work under 5 kW CW. Finally, a brief conclusion is given.

Calculation of the physical size and microwave simulation
The foremost challenge of the design of the Teflon water load is that Teflon cannot stand high temperature compared with ceramics, and enlarging the propagating cutting plane is a common method to reduce the power loss density. In the 4.6 GHz LHCD system in EAST, all the microwave structures are connected by WR229 rectangular waveguides (58.2 mm × 29.1mm), and the water load cutting plane was expanded to a circle with a radius of 50 mm (see Fig. 2). while the effect is that the microwave would propagate in several different modes. The cutting wavelengths [12] of circular waveguide can be calculated by where the R is the radius of the circular waveguide and

Power loss density of water
The power loss density of water under the input power of 0.5 W (default) simulated by CST microwave studio is shown in Fig. 4, and the X direction is the propagating direction. It is clear that the power loss density obeys Gauss2D function in YOZ cutting plane, the equal phase plane (shown in x=25mm). And according to the skin effect, it would obey exponential function along the transmission direction. The power loss density of the water was fitted with these functions by Origin software, and the fitted results are reported in Fig. 5. Compared with the central area, power loss densities in other areas are less than one forth, which would be ignored in fitted functions.    It is indicated that the Adj. R-Square are 0.99385 and 0.99453 separately, which means that the fitting results are extremely successful. The fitted functions are reported in Table 1.

Power loss density of the Teflon
Since the power loss density in the Teflon is less than 0.1 percent compared to it in the water, it is hard to observe the distribution functions in the Teflon. So E-field distribution is used to calculated the power loss density distribution in the Teflon. The power loss can be calculated by

Fluid and thermal analysis
In the actual engineering design, it is necessary to preserve the margin to ensure the safety situation. For 4.6 GHz LHCD system in EAST, the power capacity of the water load must reach 5 kW at the port 4 of the circulator. Taking the requirements of the 4.6 GHz LHCD water system in EAST into consideration, the radius of the water pipe is 10 mm, and the velocity of the water at the inlet should be less than 2 m/s to reduce the mechanical noise. According to formula the temperature increase ΔT would be only 2 ℃ under the 5 kW input power, where P is the input power, c is the specific heat capacity of water, S is the cross-sectional area of pipe, v is the velocity of the water, and ρ is the density of water. However, the thermal conductivity of Teflon is only 0.25 W/m, which would cause there is a huge temperature difference between the Teflon and the water, since that the heat generated in the Teflon can hardly be transferred to the water.  Adjusting the angle of the input water pipe to make the water take the heat generated in the water away rapidly, setting the inlet velocity, outlet pressure and the room temperature to 2 m/s, 0.5MPa and 20 ℃ separately, multiplying the fitted functions by 10000 to get UDF (user defined function) under input power of 5 kW and compiling the UDF in ANSYS Fluent to simulate the heat distribution of the Teflon water load. Simulated result is given in Fig. 8. It is indicated that the maximum temperature of the water load is 70.32 ℃, located at the center of the Teflon. Importing these results to ANSYS Static Structural Unit to get the thermal deformation and stress, it can be observed that maximum deformation and stress are only 0.139 mm and 3.19 MPa, respectively, see Fig. 9. The tensile yield strength of Teflon is 20 MPa [13], which means that the Teflon has the ability to stand the stress under input power of 5 kW. The parameter "t" (total thickness of the Teflon) sweeping result is given in Fig. 10, which shows that the microwave performance is almost unaffected by the error of 0.15 mm (maximum thermal deformation).

Conclusion
A 5 kW Teflon water load is designed for the 4.6 GHz LHCD system in EAST, taking the microwave theory and fluid thermal analysis into consideration simultaneously. The UDF was written by fitting the distribution of the E-filed and the power loss density, final simulated results indicate that this water load can absorb more than 99 percent energy under 4.6 GHz 5 kW microwave with little thermal deformation and sustainable stress.