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Power monitor miter bends for high-power microwave transmission
Fusion Engineering and Design 93 (2015) 1–8
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Power monitor miter bends for high-power microwave transmission John Doane ∗ , James Anderson, Howard Grunloh, Wen Wu General Atomics, Magnetic Fusion Energy, 3550 General Atomics Court, San Diego, CA 92121, United States
a r t i c l e
i n f o
Article history: Received 21 October 2014 Received in revised form 16 January 2015 Accepted 19 January 2015 Available online 4 March 2015 Keywords: ECH heating Corrugated waveguides Power monitors
a b s t r a c t Two miter bends are described for monitoring the power transmitted in an oversized corrugated waveguide. One has an array of holes in its mirror that couples a small fraction of the incident power to a rectangular waveguide directly machined into the mirror. Millimeter-wave detectors on the outputs of this miter bend can respond very rapidly to the transmitted power, but the coupling is sensitive to the mode purity in the oversized waveguide. The other miter bend monitors the power by measuring the rise in temperature of the cooling water passing through the mirror. The mirror is well isolated from the miter bend housing to prevent heat from neighboring waveguides from reaching the mirror. The measurement requires about 200 s to reach steady state, but it is relatively insensitive to mode purity. The measurement does require knowledge of the input polarization. Thermo-mechanical analyses of the miter bends indicate that they are capable of reliable operation with 1.5 MW transmitted through them. High-power long-pulse 170 GHz tests of these miter bends at the Japan Atomic Energy Agency (JAEA) are described. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Power monitors in high-power waveguide transmission lines have been used for three main purposes: (1) monitoring the performance of the microwave source, typically a gyrotron or gyroklystron; (2) protecting the microwave source by turning it off when significant amounts of power are detected that is traveling back toward the source; and (3) determining the power delivered to the load, which is typically a plasma or antenna. For the first two of these purposes, fast response time is normally required. If the pulse length of the source is relatively short, then determining the power delivered to the load also requires a relatively quick response. Power monitors have generally used two major techniques to couple a fraction of the high-power transmission into a low power detector: (1) multiple coupling holes in the mirror of a waveguide miter bend; and (2) a shallow diffraction grating in a mirror. In a waveguide miter bend with coupling holes, the coupled power passes through cutoff holes in the mirror and is typically focused by a thin fused quartz lens into a standard gain microwave horn [1]. The fused quartz can be sealed with epoxy to the mirror to allow evacuation of the miter bend waveguide. Shallow diffraction grating mirrors have been incorporated into waveguide miter bends
∗ Corresponding author. Tel.: +1 3013629097. E-mail address: [email protected] (J. Doane). http://dx.doi.org/10.1016/j.fusengdes.2015.01.012 0920-3796/© 2015 Elsevier B.V. All rights reserved.
without vacuum seals [2]. Shallow diffraction gratings can also be convenient in non-evacuated quasi-optical transmission lines [3] where it is relatively easy to detect the radiation reflected from the grating at the angle of the diffraction lobe. With both techniques, the coupled power originating from forward and reverse traveling high power exits the mirror in different directions and so can be detected separately. Both techniques also provide rapid response when the coupled power is detected by diode detectors. Similar techniques image the entire field propagating in the high-power transmission line. In a miter bend, an array of coupling apertures across the entire mirror can provide a coupled output that is the image of the field in the evacuated high-power waveguide [4]. By tapering the output down to single-mode or few-mode waveguide, the relative power in various low-order modes can in principle be determined. In such a manner, the alignment of the microwave beam in the high-power waveguide can be monitored. A grating coupler can be used for the same purpose on a mirror in a non-evacuated quasi-optical transmission line [5]. While the original multiple-hole coupling arrangement has been used extensively in waveguide transmission lines, it does have limitations. First, because there are typically only a small number of coupling holes, the coupling can be very sensitive to mode impurity. The coupling ratio is typically calibrated against the dominant HE11 mode propagating in corrugated waveguide. However, if a few percent of the incident power is in other HE1n modes, the ratio of coupled power to incident power can change by several dB. This is not a serious drawback if one is only interested in a qualitative
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monitoring of the microwave source or reflected power. Since the coupling holes are located near the center of the mirror, the coupling is also not affected significantly by most non-HE1n modes (including LP1n modes), because those modes do not have significant power near the center of the waveguide. A second limitation arises because the mirror must be thin in the region of the coupling holes. The coupling holes must be cutoff to the incident microwave power in order to prevent serious leakage through the mirror. Hence the hole diameter must be somewhat less than the microwave wavelength. On the other hand, cutoff holes generally attenuate the coupled power by almost 32 dB times the ratio of the length of the hole to its diameter. In order to couple enough power, the length of holes must then not exceed a wavelength. Cooling the region near the holes then becomes difficult. With high power transmission, the thermal stresses near the coupling holes can easily exceed the yield strength of the mirror material and can eventually cause localized cracking of the mirror. To improve the cooling near the coupling holes, a small coupled rectangular waveguide can be machined parallel to the surface of the mirror from one edge to the other. With arrangement, it is not necessary to remove all the material behind the entire array of coupling holes. A mirror with a coupled rectangular waveguide for a non-evacuated miter bend has previously been described [6]. A prototype mirror with five coupled rectangular waveguides at five different locations in the mirror was recently fabricated to determine the coupling to HE12 and LP11 modes as well as to HE11 by suitable combinations of the outputs [7]. This mirror also was intended for non-vacuum use. A power monitor miter bend (PMMB) with a coupled rectangular waveguide designed for an evacuated waveguide transmission line is described in this paper. With the advent of long-pulse gyrotron sources, another power monitoring arrangement becomes feasible; namely, monitoring the power absorbed in the mirror. The absorbed power is monitored calorimetrically through the water used to cool the mirror. Such a technique was described in principle many years ago, and has been implemented in large mirrors for free-space quasi-optical transmission [8]. For linearly-polarized modes, the absorbed power depends in a known way on the incident polarization. Hence if the incident polarization is known, then the incident power can be determined. This approach also requires that the mirror be well isolated from the housing of a miter bend. Otherwise, power absorbed in the neighboring waveguide could reach the mirror. This paper also describes a calorimetric miter bend (CMB) for evacuated waveguide with the required construction. One advantage of the CMB relative to the multiple-hole PMMB is that it is relatively inexpensive to fabricate. After describing the basic construction of the PMMB and CMB, the results of thermal modeling are presented. Finally, the results of high-power long-pulse tests of both the CMB and the PMMB at 170 GHz are presented.
2. Miter bend construction The multi-hole PMMB mirror is machined from one piece to allow efficient cooling. The mirror includes an array of cutoff coupling holes near the center of the mirror that are drilled through to a rectangular waveguide parallel to the mirror surface. The region around these coupling holes experiences the highest heat loading and thermal stress. Cooling channels are machined close to the mirror surface to provide good heat transfer near these coupling holes. A channel on each side of the coupling holes is directed toward the center of the mirror from the mirror edge, making a channel with an overall V-shape; the point of the V is near the mirror center. The two channels are connected externally by a loop of copper tubing.
Fig. 1. Power monitor miter bend (PMMB), showing water cooling line and output port in small circular waveguide. A transition to WR6 rectangular waveguide, a level set attenuator, and a WR6 detector are normally connected to this port.
Copper–chromium–zirconium alloy is used to provide high yield strength with little degradation in conductivity. The coupling is designed to respond only to the component of the high power input that is polarized perpendicular to the plane of the miter bend, since that polarization produces the lowest ohmic loss on the mirror. The width of the rectangular waveguide perpendicular to the electric field must match the phase velocity of the TE10 mode in rectangular waveguide to the component of the high power input parallel to the mirror surface. For 45◦ incidence √ as in a miter bend, the width must then be / 2. At 170 GHz where the wavelength is 1.764 mm, the corresponding width is 1.25 mm. For convenience in machining the waveguide into the mirror by a wire EDM process, the other dimension of the waveguide was made large enough to propagate the rectangular waveguide TE01 mode. Nevertheless, the phase velocity of that cross-polarized mode was sufficiently mismatched to the high power input that it would not be excited. A transition to circular waveguide and a circular waveguide uptaper are machined into the mirror at each end of the rectangular waveguide in order to reduce the effect of the discontinuities at vacuum windows. Each window consists of a small disk of fused silica sealed with a Helicoflex® metal seal. On the atmospheric side of the window a separate circular waveguide downtaper to relatively small circular waveguide is attached. The fused silica window material is chosen to be fairly lossy in order to minimize the effect of any modes trapped between the tapers on either side. A standard commercial transition between the circular and fundamental WR6 waveguide completes the mirror assembly. Since the construction is symmetric, the mirror can be used to detect power in the reverse as well as the forward direction in the high power waveguide. In order to allow space for flanges for the output tapers at the windows, the central part of the mirror is recessed. The miter bend housing is inserted into that recess. The entire power monitor assembly is shown in Fig. 1. The calorimetric miter bend uses reentrant cooling through a small-diameter shaft in order to keep the mirror isolated as much as possible from the miter bend housing. A rotatable water union allows a convenient connection of the external water-cooling tubing to the mirror. This union is the same as used in polarizer miter bends. However, in the calorimetric miter bend the union is not actually rotated. A thin-walled stainless steel cylinder provides high thermal resistance between the rear of the mirror assembly and the main part of the miter bend housing. Deep water channels are machined into the thicker rear part of this cylinder to short circuit the flow of any residual heat heading toward the rear of the mirror assembly. A
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Fig. 2. Calorimetric miter bend (CMB), showing separate cooling lines for the miter bend housing, the stainless steel isolation housing, and the mirror.
separate water circuit can monitor this residual heat. Finally, copper cooling plates attached to the miter bend housing itself allow monitoring of the heat absorbed in the housing. Fig. 2 shows the completed calorimetric miter bend assembly. 3. Thermal analyses The ANSYS analyses assumed that the initial distribution of absorbed power on the mirrors corresponded to pure HE11 incident on the mirror. The heated region of the mirrors is elliptical, since the power is incident at a 45◦ angle. The absorption was then corrected for the local surface temperature, assuming that the surface resistance is proportional to the square root of the absolute temperature. This assumption amounts to assuming that the local electric resistivity of the mirror is proportional to the absolute temperature, which is a good approximation for copper alloys. No temperature correction for the thermal conductivity was made, since it varies little up to 300 ◦ C in copper. These analyses assumed that the mirror material was C18150 CuCrZr alloy with 324 W/m K thermal conductivity. The typical electrical conductivity of C18150 is about 85% of ideal copper. No correction was made for surface roughness of the mirror. However, room temperature measurements at 170 GHz of a copper mirror polished to 0.2 m indicated that the mirror absorption was only about 6% higher than that predicted for ideal copper [9]. Analysis of the CuCrZr PMMB mirror was performed for the following conditions: 1700 W total absorption at room temperature, 24 l/min water flow, and 27 ◦ C inlet water temperature. This absorption corresponds to about 2 MW transmission with the electric field perpendicular to the plane of the bend. After correction for the temperature rise of the mirror, the steady state total absorption was then about 1800 W. The ANSYS results indicated that the peak PMMB mirror surface temperature was 77 ◦ C with less than 50 ◦ C variation from center to edge. The maximum stress was 178 MPa. By comparison, the yield strength of CuCrZr alloy is typically 360 to 430 MPa at 100 ◦ C [10]. In large diameters, the yield strength is typically somewhat lower.
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The corresponding strain is about 0.15%, which leads to an expected life of the mirror on the order of 100,000 cycles [11]. The deflection of the mirror surface from the center to the edge of the elliptical heated zone was about 12 m. This deflection would lead to only about 0.015% mode conversion, according to the analysis outlined in Appendix A. The distributions of both the temperature increase and the deformation match the elliptical shape of the heated region on the mirror, and both are quite small. Analysis of a CuCrZr CMB mirror was performed for the following conditions: 2600 W total absorption at room temperature, 24 l/min water flow, and 27 ◦ C inlet water temperature. The absorption corresponds to about 1.5 MW transmission with the worst case incident polarization (with the electric field in the plane of the bend). The steady state total absorption was then about 3100 W. The ANSYS results shown in [Fig. 3(a)] indicated that the peak mirror surface temperature was 163 ◦ C with less than 30 ◦ C variation over the elliptical-shaped heated region heated by the incident microwaves. This region, outlined in black in Fig. 3a, has width 63.5 mm and length 89.8 mm. Since the cooling water impinges on the center of the mirror, the peak temperatures actually occur somewhat away from the center, even though the peak heat loading is at the center. The maximum stress was less than 250 MPa, corresponding to about 0.22% strain. Hence the expected life of the mirror is on the order of 100,000 cycles [12]. As shown in Fig. 3b, the deflection of the mirror surface varied only about 15 m over the heated region. This deflection would also lead to negligible mode conversion.
4. High power test results The Naka site of the Japan Atomic Energy Agency (JAEA) has a test stand powered by a long-pulse 170 GHz gyrotron. A schematic of the test stand layout is shown as Fig. 4. Key components include a polarizer miter bend (PMB) located at the first miter bend location in the 4 miter bend ‘dogleg.’ The PMMB and CMB were separately tested at the last miter bend location before the dummy load (see Fig. 5). The waveguide switches were always set to direct the power to these miter bends for these tests. The polarization incident on the PMB is always horizontal, perpendicular to the plane of the PMB bend. The groove geometry of this polarizer allows the input polarization to be rotated by rotating the mirror. By convention, the grooves in the PMB are perpendicular to its bend plane when its mirror rotation angle is zero. A positive mirror rotation angle corresponds to clockwise rotation of the mirror when viewing the polarizer miter bend from behind its mirror. When the mirror rotation angle is 0◦ or 90◦ , the input polarization is not affected. When the mirror rotation angle is about ±55◦ , then the input polarization is rotated by 90◦ and exits the PMB parallel to its bend plane. For other mirror rotation angles, the output polarization is not purely linear but contains a small elliptical component. If the PMB did not change the horizontal input polarization, then the polarization incident at the last miter bend would also be horizontal. However, the PMMB only responds to the electric field that is parallel to its bend plane. Hence the required polarization at the location of this miter bend must be vertical. To establish that condition, the PMB mirror rotation angle was set to −54.7◦ . Fig. 6 shows the outputs of the WR6 detectors connected to the PMMB for a 240-s pulse with about 350 kW of 170 GHz incident power. A WR6 attenuator set to 19.5 dB attenuation was located before the WR6 detector for the forward coupled power, whereas no attenuator was in the path to the WR6 detector for the reverse coupled power. While the detectors were not calibrated, they were from the same lot and typically have similar sensitivities. Hence, from Fig. 6 it can be concluded that the directivity of the PMMB is
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Fig. 3. Steady-state ANSYS results for the calorimetric miter bend of Fig. 2, assuming 2600 W total room temperature absorption on a C18150 copper chromium zirconium mirror with 0.6 l/s flow. The mirror surface is colored, and the z-axis is along the major axis of the heated elliptical region. (a) Temperature distribution on mirror surface; (b) deformation of mirror surface.
greater than 20 dB. The gradual drop in the signal during the pulse is correlated with a slight drop in the gyrotron power. To measure the power absorbed in a mirror, the difference T in the input and output mirror cooling water temperatures in degrees C is multiplied by the flow F in liters per second and the heat capacity of water near room temperature: Pabs = 4184 F T watts
(1)
The water temperatures were measured with resistance temperature detectors (RTDs) inserted into the cooling lines through Swagelok® tee fittings. The flow meter was a vortex type. The data labeled absorbed power in the following figures actually is just the data calculated by Eq. (1), normalized to the input power. The input power was determined from calorimetric measurements at the dummy load. Generally more than 100 s was required for the data calculated by Eq. (1) to reach steady state. The power absorbed in the PMB mirror for a −54.7◦ mirror rotation angle is shown in Fig. 7 for a 240-s pulse test of the PMMB and for a 400-s pulse test of the CMB. The indicated absorbed power
(0.54%) is virtually identical for the two cases. Note that the power absorbed in the PMB mirror is much higher than the room temperature theoretical value (0.23%). In general, the theoretical and measured power absorbed in this mirror increased with increased mirror rotation angle. When the mirror rotation angle was 0◦ , the measured power absorbed in the PMB mirror was just a few percent higher than the room temperature theoretical value (0.124%). Calculations of the theoretical power absorption in the PMB mirror were based on space harmonic field calculations [13]. In previous tests in 2010, the power absorbed in the PMB mirror did not reach steady state when the incident power was about 600 kW and the mirror rotation angle was more than about 50◦ . Since the PMB mirror is well isolated from the polarizer housing, this result indicated that there might be a thermal runaway situation. The water flow was about 12 l/min for those tests. In the present tests, the water flow was restricted to only 9 l/min. Hence for the tests described in this paper, the power level was lowered to about 350 kW. For 1 MW operation with arbitrary mirror rotation angles, greater water flow will be required. In addition, a newer
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Fig. 4. Test line with long-pulse high-power 170 GHz gyrotron at the Japan Atomic Energy Agency fusion research facility in Naka. The PMMB and CMB power monitor miter bends were tested separately at the location indicated.
Fig. 5. PMMB power monitor installed in the test line of Fig. 4.
Fig. 6. Signals from the WR6 diode detectors on the forward (top curve) and reverse (lower curve) coupled ports of the PMMB. A WR6 attenuator set for 19.5 dB attenuation was placed before the detector of the forward coupled power. No attenuator was placed before the detector of reverse coupled power. The 170 GHz input power was approximately 350 kW.
design of the polarizer mirrors provides greater radial cooling than is possible in the polarizers used in these tests. The absorbed power in the PMMB and CMB are compared in Fig. 8 for the same case as in Fig. 7, which shows the power absorbed in the polarizer (PMB). The vertical axis is labeled as the fractional absorbed power, in accordance with Eq. (1). The theoretical room temperature absorption is only 0.08% for a copper mirror in this case, where the incident electric field is perpendicular to the plane of the PMMB or CMB bends. (The theoretical absorption is only slightly higher for the CuCrZr mirror in the PMMB.) The water temperature rise for the CMB reaches a steady state, because the mirror in that bend is well isolated from the miter bend housing, just as the mirror in the polarizer miter bend is well isolated from its miter bend housing. However, in the PMMB the water temperature rise never approaches a steady state. The mirror in the PMMB is directly connected to the miter bend housing. Hence power absorbed in the housing or nearby waveguides could be conducted to the mirror. In particular, the 2-m waveguide between the closest waveguide switch and the PMMB became anomalously hot during these tests. An explanation for this high waveguide heating is discussed separately [14] in terms of mode conversion caused by powerdependent misalignments. Even if such anomalous heating existed in a CW transmission line, all waveguides in such a line will be
Fig. 7. Power absorbed in polarizer miter bend when polarizer mirror rotation angle was set for −54.7◦ for tests of the PMMB and CMB power monitor miter bends. The longer pulse was for the CMB test. The line marked “Theory” is the calculated room temperature absorption on the polarizer mirror for an ideal grooved surface.
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Acknowledgments This work was supported by General Atomics Internal Research and Development funding. The high-power tests reported here were performed at the Japan Atomic Energy Agency (JAEA) at Naka, Japan. The authors gratefully acknowledge the assistance of Koji Takahashi, Keishi Sakamoto and the other JAEA staff who worked long hours each day to help complete the measurements. The reliability of the JAEA 170 GHz gyrotron was essential. Appendix A. Estimate of mode conversion loss due to distortion of miter bend mirror
Fig. 8. Power absorbed in PMMB and CMB mirrors when the polarizer mirror was set as in Fig. 7. The line marked “Theory” is the calculated room temperature absorption on a flat mirror with an ideal smooth surface when the incident electric field is perpendicular to the plane of the miter bend.
Assume the situation with the HE11 mode in a miter bend can be modeled approximately with an equivalent Gaussian beam. The best approximation of a Gaussian to an HE11 mode is with a beam radius of w = 0.32D,
(A1)
where D is the waveguide diameter. For a simple miter bend, the radius of curvature Ri of the equivalent Gaussian beam incident on the mirror is infinite. That is, its phase front is planar. Next, assume that the distorted mirror can be modeled as a portion of an ellipsoidal surface, as shown in Fig. A1. This figure shows a concave distortion, but a convex distortion should give a similar result. The dashed lines show the incident and reflected rays in the plane of the miter bend. For incidence at 45◦ as in a miter bend, the ellipsoidal surface can be described as follows Z2 X2 + Y 2 + 2 =1 B2 A Fig. 9. Fractional power absorbed on CMB mirror as a function of the polarizer mirror rotation angle.
cooled. That cooling will prevent excessive heat from reaching adjacent miter bend mirrors. Notice in Fig. 8 that the steady state indication of absorbed power in the CMB is only a little higher than the theoretical value. The results with a total of 11 different settings of the PMB mirror rotation angle are summarized in Fig. 9. The theoretical roomtemperature absorbed power in Fig. 9 is determined from Eq. (B7) of Appendix B and the theoretical polarization parameters corresponding to the PMB mirror rotation angles. An additional curve 20% higher than the room temperature values has been added; this curve fits the data reasonably well. Since the bulk resistivity of a copper mirror is approximately proportional to the absolute temperature, the surface resistance and hence the local absorbed power should be approximately proportional to the square root of the local absolute temperature. For ◦ example, a 100 ◦ C temperature rise from 27 ◦ C (300 K) should cause the absorbed power to increase by a factor of 400/300 = 1.155, corresponding to a 15.5% increase.
where √ A = 2B.
(A3)
where Z is measured along the axis of rotation of the ellipsoid, in the plane of the miter bend. X is also in the plane of the bend, and Y is perpendicular to the plane of the bend. The dimension E is equal to the square root of 2 times the waveguide diameter D. At the edge of the miter bend mirror in the Y = 0 plane, we have from Eq. (A2) and Fig. A1
2
B−ı B2
+
(0.5E)2 = 1. A2
(A4)
√ Using Eq. (A3) and E = 2D, we find from Eq. (A4) after neglecting the term in the square of the deflection that A=
D2 √ 4 2ı
(A5)
At the edge of the mirror in the X–Y plane at Z = 0, we must have X = B − ı, and Y = D/2. A simple calculation using Eqs. (A3) and (A5) verifies that Eq. (A2) is satisfied in this case. Hence the ellipsoidal
5. Conclusions High-power long-pulse tests as well as thermomechanical analyses indicated that the miter bends described in this paper are suitable for monitors of power in transmission lines similar to those planned for ITER. One miter bend (“power monitor miter bend” or PMMB) is suitable for rapid response to changes of both forward power and stray reflected power. The other miter bend (“calorimetric miter bend” or CMB) can accurately measure absolute power in long pulses. A single point calibration of the CMB against a dummy load can be useful; otherwise, only knowledge of the incident polarization is required for the measurement.
(A2)
Fig. A1. Geometry of deformed mirror surface.
J. Doane et al. / Fusion Engineering and Design 93 (2015) 1–8
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surface outlined here is a reasonable model of a miter bend mirror with deflection ı at its center. Noting that the focal length of the ellipsoidal surface described above is f = A/2 [15], we can now use the simple focal length formula 1 1 1 + = Ri Rr f
(A6)
where Ri and Rr are the radii of curvature of the incident and reflected beam, respectively, to find that Rr =
A D2 = √ , 2 8 2ı
(A7)
since Ri is infinite. The efficiency of coupling between two Gaussian beams with normalized amplitudes u1 (x,y) and u2 (x,y) is
2 ∞ 2 2 = u1 • u∗2 = d rdru1 u∗2 0
Fig. B1. Coordinate systems near mirror.
(A8)
0
At the miter bend mirror, the equivalent beams have the same beam radius and differ only in the radii of curvature. Let ui and ur represent the beams incident and reflected from the miter bend mirror, respectively. At the mirror we can write:
ui ∼exp and
−r 2 w2
ur ∼exp −r 2
(A9a)
1 w2
+j
Rr
Carrying out the integration in Eq. (A8), we find
=
1+
w2 2Rr
2 −1
∼ =
1−
w2 2Rr
2 (A10)
Inserting Eqs. (A1) and (A7) into Eq. (A10) and assuming that the deflection is much smaller than a wavelength , we find
2
∼ = 1 − 3.3
ı
(A11)
Since the mode conversion loss MCL is 1 − , the loss is
2
MCL ∼ = 3.3
ı
Fig. B2. Definition of polarization.
(A9b)
(A12)
A similar result was obtained by Michael Shapiro using analysis similar to that developed elsewhere [16]. For example, if the deflection is 0.04 mm at 170 GHz where the wavelength is 1.763 mm, MCL is 0.0017, or 0.17%. This is less than the mode conversion in an ideal miter bend with a flat mirror, which is 0.26% at 170 GHz in 63.5-mm waveguide. Appendix B. Theoretical dependence on input polarization of power absorbed on a miter bend mirror First let us define two coordinate systems as follows. Let the ˆ in the ϕ direction be perpendicular to the plane of unit vector ϕ ˆ where kˆ is the unit incidence, and define the unit vector ˆ as ϕ ˆ × k, vector in the propagation direction. Further, relative to the polarizer mirror define a right-handed coordinate system (ˆx, yˆ , zˆ ) where zˆ is ˆ is in the vertical direction normal to the mirror surface, and yˆ = ϕ perpendicular to the plane of incidence. See Fig. B1. Letting zˆ point away the mirror, then in terms of the incidence angle , ˆ = xˆ cos + zˆ sin.
Next we write the polarization incident on the mirror in terms of a polarization ellipse. The orientation of its major axis is rotated from ˆ clockwise by an angle ˛ (looking along the propagation ˆ and it has an ellipticity ˇ defined as the tangent of direction k), the ratio of the minor to major axes of the ellipse. See Fig. B2. The domains of these angles are 0 ≤ ˛ < 180◦ , and −45◦ ≤ ˇ ≤ 45◦ . With spatial and time dependence exp [j(ωt − k )] assumed, where is distance along the propagation direction, we can write the incident electric field components apart from a constant amplitude as: e = cos˛cosˇ + jsin˛sinˇ
(B1a)
eϕ = sin˛cosˇ − jcos˛sinˇ
(B1b)
Similarly, since the incident power flow is in the kˆ direction, we then have Z0 h = sin˛cosˇ + jcos˛sinˇ = −eϕ
(B2a)
Z0 hϕ = cos˛ cosˇ + jsin˛ sinˇ = −e
(B2b)
Then in terms of the (ˆx, yˆ , zˆ ) coordinates h = xˆ h cos + yˆ hϕ + zˆ h sin
(B3)
The surface current density on the mirror is equal to the total tangential magnetic field on the mirror, which is double the tangential component of the incident magnetic field. In terms of the incident magnetic field given by Eq. (B3) and the unit vector normal to the mirror surface nˆ = zˆ , the current density is J = 2nˆ × h = −2ˆxhϕ − 2ˆyh cos
(B4)
The fractional power ohmic loss on the mirror surface can be calculated by integration of the surface current over the mirror as follows:
PL =
Rs /2
| J|2 dA
Pi Acos
,
(B5)
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where Pi is the incident power, is the angle of incidence, and Rs is the mirror surface resistance. From Eqs. (B2) and (B4), the squared current is
|J|2 = 4/Z02
1 − sin2 cos2 ˇsin2 ˛ + sin2 ˇcos2 ˛
(B6)
The incident power is Pi = (1/2)e × h, which from Eqs. (B2) is equal to 1/(2Z0 ). Hence the fractional loss is PL = 4
R [1 − sin2 (cos2 ˇsin2 ˛ + sin2 ˇcos2 ˛)] s Z0
cos
(B7)
In particular, if the incident electric field is linearly polarized in the plane of incidence (“E-plane” case) so that ˛ = ˇ = 0◦ then the term in square brackets in Eq. (B6) is unity. The magnetic field in that case is perpendicular to the plane of incidence and hence parallel to the mirror, so that all the incident field contributes to current on the mirror. If the incident electric field is linearly polarized perpendicular to the plane of incident (“H-plane” case), then ˛ = 90◦ , and the same sum is only cos2 . For = 45◦ as in a miter bend, then this sum is only 0.5. This result corresponds to the fact that some of the incident magnetic field is perpendicular to the mirror and hence does not contribute to the current. Eq. (B7) reduces to the familiar results 4(Rs /Z0 )/cos and 4(Rs /Z0 )cos for the E-plane and H-plane cases, respectively. The term 4(Rs /Z0 ) is simply the fractional loss on a flat mirror at normal incidence. For a circularly polarized input ˇ = 45◦ , and so for a typical miter bend with = 45◦ , the fractional loss is 4(Rs /Z0 )(1.06). In terms of the bulk resistivity and the free space wavelength , the surface resistance is
Rs =
Z0
(B8)
The effective surface resistance can be increased by surface roughness. References [1] J.L. Doane, R.A. Olstad, Transmission line technology for electron cyclotron heating, Fusion Sci. Technol. 53 (2008) 39–53 (Fig. 5). The first power monitor of this type was designed by Charles Moeller of General Atomics.
[2] V.I. Malygin, V.I. Belousov, A.V. Chirkov, G.G. Denisov, M.Yu. Shmelyov, I.V. Kurbatov, I.V. Kazanskiy, E.A. Solujanova, E.M. Tai, Transmission lines for microwave radiation of powerful continuous wave gyrotrons, in: Proc. 29th Int’l. Conf. Infrared and Millimeter Waves, Sept. 27–Oct., 2004, Institute of Electrical and Electronics Engineers, Karlsruhe, Germany, 2004, pp. 221–222. [3] V. Erckmann, et al., Electron cyclotron heating for W7-X: physics and technology, Fusion Sci. Technol. 52 (2007) p291ff. [4] C. Moeller, M. Cengher, Y. Gorelov, J. Lohr, Power and mode diagnostics for 110 GHz, in: National Gyrotron/ECH Technology Workshop, 26–27 Jan, 2011, San Diego, California, 2011. [5] J. Shi, W. Kasparek, A grating coupler for in-situ alignment of a Gaussian beam—principle, design, and low-power test, IEEE Trans. Antennas Propag. 52 (2004) 2517–2524. [6] L. Empacher, W. Förster, G. Gantenbein, W. Kasparek, H. Kumric, G.A. Müller, P.G. Schüller, K. Schwörer, D. Wagner, New developments and tests of high power transmission components for ECRH on ASDEX upgrade and W7-AS, in: Proc. 20th Int. Conf,. Infrared and Millimeter, Waves, Orlando, Florida, 1995, pp. 473–474. [7] J. Ruiz, W. Kasparek, C. Lechte, B. Plaum, H. Idei, Numerical and experimental investigation of a 5-port mitre-bend directional coupler for mode analysis in corrugated waveguides, J. Infrared, Millimeter, Terahertz Waves 33 (2012) 491–504. [8] W. Kasparek, D. Arz, L. Empacher, V. Erckmann, G. Gantenbein, F. Hollman, P.G. Schüller, K. Schwörer, M. Weissgerber, Performance of the 140 GHz prototype transmission system for ECRH on the stellarator W7-X, Fusion Eng. Des. 56–57 (2001) 621–626. [9] Reported in M.A. Henderson, “Miter Bend test programme,” draft of unpublished memo, 19 Feb. 2007, based on measurements at the University of Stuttgart on equipment described in W. Kasparek, A. Fernandez, F. Hollman, and R. Wacker, “Measurements of Ohmic Losses of Metallic Reflectors at 140 GHz Using a 3-Mirror Resonator Technique,” Int. J. Infrared Millimeter Waves, 22, (2001) 1695-1706. [10] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690 (Section 4.20; Fig. 3). [11] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690, Fig. 6. [12] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690. [13] John Doane, Howard Grunloh, Ward Martin, Wen Wu, “Polarizer miter bends for high-power microwave transmission: ohmic loss and cooling,” in preparation for publication. [14] P. Anderson, et al., Recent component development at GA for ITER ECH transmission lines, in: US-EU-Japan RF Heating Technology Workshop, September 2014, Sedona, AZ, 2014. [15] P.F. Goldsmith, Quasioptical Systems, IEEE Press, Piscataway, NJ, 1998, pp. 109–110 (for example). [16] E. Kowalski, M.A. Shapiro, R.J. Temkin, Simple correctors for elimination of highorder modes in corrugated waveguide transmission lines, IEEE Trans. Plasma Sci. 42 (2014) 29–37 (Sections V and VI).
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Power monitor miter bends for high-power microwave transmission John Doane ∗ , James Anderson, Howard Grunloh, Wen Wu General Atomics, Magnetic Fusion Energy, 3550 General Atomics Court, San Diego, CA 92121, United States
a r t i c l e
i n f o
Article history: Received 21 October 2014 Received in revised form 16 January 2015 Accepted 19 January 2015 Available online 4 March 2015 Keywords: ECH heating Corrugated waveguides Power monitors
a b s t r a c t Two miter bends are described for monitoring the power transmitted in an oversized corrugated waveguide. One has an array of holes in its mirror that couples a small fraction of the incident power to a rectangular waveguide directly machined into the mirror. Millimeter-wave detectors on the outputs of this miter bend can respond very rapidly to the transmitted power, but the coupling is sensitive to the mode purity in the oversized waveguide. The other miter bend monitors the power by measuring the rise in temperature of the cooling water passing through the mirror. The mirror is well isolated from the miter bend housing to prevent heat from neighboring waveguides from reaching the mirror. The measurement requires about 200 s to reach steady state, but it is relatively insensitive to mode purity. The measurement does require knowledge of the input polarization. Thermo-mechanical analyses of the miter bends indicate that they are capable of reliable operation with 1.5 MW transmitted through them. High-power long-pulse 170 GHz tests of these miter bends at the Japan Atomic Energy Agency (JAEA) are described. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Power monitors in high-power waveguide transmission lines have been used for three main purposes: (1) monitoring the performance of the microwave source, typically a gyrotron or gyroklystron; (2) protecting the microwave source by turning it off when significant amounts of power are detected that is traveling back toward the source; and (3) determining the power delivered to the load, which is typically a plasma or antenna. For the first two of these purposes, fast response time is normally required. If the pulse length of the source is relatively short, then determining the power delivered to the load also requires a relatively quick response. Power monitors have generally used two major techniques to couple a fraction of the high-power transmission into a low power detector: (1) multiple coupling holes in the mirror of a waveguide miter bend; and (2) a shallow diffraction grating in a mirror. In a waveguide miter bend with coupling holes, the coupled power passes through cutoff holes in the mirror and is typically focused by a thin fused quartz lens into a standard gain microwave horn [1]. The fused quartz can be sealed with epoxy to the mirror to allow evacuation of the miter bend waveguide. Shallow diffraction grating mirrors have been incorporated into waveguide miter bends
∗ Corresponding author. Tel.: +1 3013629097. E-mail address: [email protected] (J. Doane). http://dx.doi.org/10.1016/j.fusengdes.2015.01.012 0920-3796/© 2015 Elsevier B.V. All rights reserved.
without vacuum seals [2]. Shallow diffraction gratings can also be convenient in non-evacuated quasi-optical transmission lines [3] where it is relatively easy to detect the radiation reflected from the grating at the angle of the diffraction lobe. With both techniques, the coupled power originating from forward and reverse traveling high power exits the mirror in different directions and so can be detected separately. Both techniques also provide rapid response when the coupled power is detected by diode detectors. Similar techniques image the entire field propagating in the high-power transmission line. In a miter bend, an array of coupling apertures across the entire mirror can provide a coupled output that is the image of the field in the evacuated high-power waveguide [4]. By tapering the output down to single-mode or few-mode waveguide, the relative power in various low-order modes can in principle be determined. In such a manner, the alignment of the microwave beam in the high-power waveguide can be monitored. A grating coupler can be used for the same purpose on a mirror in a non-evacuated quasi-optical transmission line [5]. While the original multiple-hole coupling arrangement has been used extensively in waveguide transmission lines, it does have limitations. First, because there are typically only a small number of coupling holes, the coupling can be very sensitive to mode impurity. The coupling ratio is typically calibrated against the dominant HE11 mode propagating in corrugated waveguide. However, if a few percent of the incident power is in other HE1n modes, the ratio of coupled power to incident power can change by several dB. This is not a serious drawback if one is only interested in a qualitative
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monitoring of the microwave source or reflected power. Since the coupling holes are located near the center of the mirror, the coupling is also not affected significantly by most non-HE1n modes (including LP1n modes), because those modes do not have significant power near the center of the waveguide. A second limitation arises because the mirror must be thin in the region of the coupling holes. The coupling holes must be cutoff to the incident microwave power in order to prevent serious leakage through the mirror. Hence the hole diameter must be somewhat less than the microwave wavelength. On the other hand, cutoff holes generally attenuate the coupled power by almost 32 dB times the ratio of the length of the hole to its diameter. In order to couple enough power, the length of holes must then not exceed a wavelength. Cooling the region near the holes then becomes difficult. With high power transmission, the thermal stresses near the coupling holes can easily exceed the yield strength of the mirror material and can eventually cause localized cracking of the mirror. To improve the cooling near the coupling holes, a small coupled rectangular waveguide can be machined parallel to the surface of the mirror from one edge to the other. With arrangement, it is not necessary to remove all the material behind the entire array of coupling holes. A mirror with a coupled rectangular waveguide for a non-evacuated miter bend has previously been described [6]. A prototype mirror with five coupled rectangular waveguides at five different locations in the mirror was recently fabricated to determine the coupling to HE12 and LP11 modes as well as to HE11 by suitable combinations of the outputs [7]. This mirror also was intended for non-vacuum use. A power monitor miter bend (PMMB) with a coupled rectangular waveguide designed for an evacuated waveguide transmission line is described in this paper. With the advent of long-pulse gyrotron sources, another power monitoring arrangement becomes feasible; namely, monitoring the power absorbed in the mirror. The absorbed power is monitored calorimetrically through the water used to cool the mirror. Such a technique was described in principle many years ago, and has been implemented in large mirrors for free-space quasi-optical transmission [8]. For linearly-polarized modes, the absorbed power depends in a known way on the incident polarization. Hence if the incident polarization is known, then the incident power can be determined. This approach also requires that the mirror be well isolated from the housing of a miter bend. Otherwise, power absorbed in the neighboring waveguide could reach the mirror. This paper also describes a calorimetric miter bend (CMB) for evacuated waveguide with the required construction. One advantage of the CMB relative to the multiple-hole PMMB is that it is relatively inexpensive to fabricate. After describing the basic construction of the PMMB and CMB, the results of thermal modeling are presented. Finally, the results of high-power long-pulse tests of both the CMB and the PMMB at 170 GHz are presented.
2. Miter bend construction The multi-hole PMMB mirror is machined from one piece to allow efficient cooling. The mirror includes an array of cutoff coupling holes near the center of the mirror that are drilled through to a rectangular waveguide parallel to the mirror surface. The region around these coupling holes experiences the highest heat loading and thermal stress. Cooling channels are machined close to the mirror surface to provide good heat transfer near these coupling holes. A channel on each side of the coupling holes is directed toward the center of the mirror from the mirror edge, making a channel with an overall V-shape; the point of the V is near the mirror center. The two channels are connected externally by a loop of copper tubing.
Fig. 1. Power monitor miter bend (PMMB), showing water cooling line and output port in small circular waveguide. A transition to WR6 rectangular waveguide, a level set attenuator, and a WR6 detector are normally connected to this port.
Copper–chromium–zirconium alloy is used to provide high yield strength with little degradation in conductivity. The coupling is designed to respond only to the component of the high power input that is polarized perpendicular to the plane of the miter bend, since that polarization produces the lowest ohmic loss on the mirror. The width of the rectangular waveguide perpendicular to the electric field must match the phase velocity of the TE10 mode in rectangular waveguide to the component of the high power input parallel to the mirror surface. For 45◦ incidence √ as in a miter bend, the width must then be / 2. At 170 GHz where the wavelength is 1.764 mm, the corresponding width is 1.25 mm. For convenience in machining the waveguide into the mirror by a wire EDM process, the other dimension of the waveguide was made large enough to propagate the rectangular waveguide TE01 mode. Nevertheless, the phase velocity of that cross-polarized mode was sufficiently mismatched to the high power input that it would not be excited. A transition to circular waveguide and a circular waveguide uptaper are machined into the mirror at each end of the rectangular waveguide in order to reduce the effect of the discontinuities at vacuum windows. Each window consists of a small disk of fused silica sealed with a Helicoflex® metal seal. On the atmospheric side of the window a separate circular waveguide downtaper to relatively small circular waveguide is attached. The fused silica window material is chosen to be fairly lossy in order to minimize the effect of any modes trapped between the tapers on either side. A standard commercial transition between the circular and fundamental WR6 waveguide completes the mirror assembly. Since the construction is symmetric, the mirror can be used to detect power in the reverse as well as the forward direction in the high power waveguide. In order to allow space for flanges for the output tapers at the windows, the central part of the mirror is recessed. The miter bend housing is inserted into that recess. The entire power monitor assembly is shown in Fig. 1. The calorimetric miter bend uses reentrant cooling through a small-diameter shaft in order to keep the mirror isolated as much as possible from the miter bend housing. A rotatable water union allows a convenient connection of the external water-cooling tubing to the mirror. This union is the same as used in polarizer miter bends. However, in the calorimetric miter bend the union is not actually rotated. A thin-walled stainless steel cylinder provides high thermal resistance between the rear of the mirror assembly and the main part of the miter bend housing. Deep water channels are machined into the thicker rear part of this cylinder to short circuit the flow of any residual heat heading toward the rear of the mirror assembly. A
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Fig. 2. Calorimetric miter bend (CMB), showing separate cooling lines for the miter bend housing, the stainless steel isolation housing, and the mirror.
separate water circuit can monitor this residual heat. Finally, copper cooling plates attached to the miter bend housing itself allow monitoring of the heat absorbed in the housing. Fig. 2 shows the completed calorimetric miter bend assembly. 3. Thermal analyses The ANSYS analyses assumed that the initial distribution of absorbed power on the mirrors corresponded to pure HE11 incident on the mirror. The heated region of the mirrors is elliptical, since the power is incident at a 45◦ angle. The absorption was then corrected for the local surface temperature, assuming that the surface resistance is proportional to the square root of the absolute temperature. This assumption amounts to assuming that the local electric resistivity of the mirror is proportional to the absolute temperature, which is a good approximation for copper alloys. No temperature correction for the thermal conductivity was made, since it varies little up to 300 ◦ C in copper. These analyses assumed that the mirror material was C18150 CuCrZr alloy with 324 W/m K thermal conductivity. The typical electrical conductivity of C18150 is about 85% of ideal copper. No correction was made for surface roughness of the mirror. However, room temperature measurements at 170 GHz of a copper mirror polished to 0.2 m indicated that the mirror absorption was only about 6% higher than that predicted for ideal copper [9]. Analysis of the CuCrZr PMMB mirror was performed for the following conditions: 1700 W total absorption at room temperature, 24 l/min water flow, and 27 ◦ C inlet water temperature. This absorption corresponds to about 2 MW transmission with the electric field perpendicular to the plane of the bend. After correction for the temperature rise of the mirror, the steady state total absorption was then about 1800 W. The ANSYS results indicated that the peak PMMB mirror surface temperature was 77 ◦ C with less than 50 ◦ C variation from center to edge. The maximum stress was 178 MPa. By comparison, the yield strength of CuCrZr alloy is typically 360 to 430 MPa at 100 ◦ C [10]. In large diameters, the yield strength is typically somewhat lower.
3
The corresponding strain is about 0.15%, which leads to an expected life of the mirror on the order of 100,000 cycles [11]. The deflection of the mirror surface from the center to the edge of the elliptical heated zone was about 12 m. This deflection would lead to only about 0.015% mode conversion, according to the analysis outlined in Appendix A. The distributions of both the temperature increase and the deformation match the elliptical shape of the heated region on the mirror, and both are quite small. Analysis of a CuCrZr CMB mirror was performed for the following conditions: 2600 W total absorption at room temperature, 24 l/min water flow, and 27 ◦ C inlet water temperature. The absorption corresponds to about 1.5 MW transmission with the worst case incident polarization (with the electric field in the plane of the bend). The steady state total absorption was then about 3100 W. The ANSYS results shown in [Fig. 3(a)] indicated that the peak mirror surface temperature was 163 ◦ C with less than 30 ◦ C variation over the elliptical-shaped heated region heated by the incident microwaves. This region, outlined in black in Fig. 3a, has width 63.5 mm and length 89.8 mm. Since the cooling water impinges on the center of the mirror, the peak temperatures actually occur somewhat away from the center, even though the peak heat loading is at the center. The maximum stress was less than 250 MPa, corresponding to about 0.22% strain. Hence the expected life of the mirror is on the order of 100,000 cycles [12]. As shown in Fig. 3b, the deflection of the mirror surface varied only about 15 m over the heated region. This deflection would also lead to negligible mode conversion.
4. High power test results The Naka site of the Japan Atomic Energy Agency (JAEA) has a test stand powered by a long-pulse 170 GHz gyrotron. A schematic of the test stand layout is shown as Fig. 4. Key components include a polarizer miter bend (PMB) located at the first miter bend location in the 4 miter bend ‘dogleg.’ The PMMB and CMB were separately tested at the last miter bend location before the dummy load (see Fig. 5). The waveguide switches were always set to direct the power to these miter bends for these tests. The polarization incident on the PMB is always horizontal, perpendicular to the plane of the PMB bend. The groove geometry of this polarizer allows the input polarization to be rotated by rotating the mirror. By convention, the grooves in the PMB are perpendicular to its bend plane when its mirror rotation angle is zero. A positive mirror rotation angle corresponds to clockwise rotation of the mirror when viewing the polarizer miter bend from behind its mirror. When the mirror rotation angle is 0◦ or 90◦ , the input polarization is not affected. When the mirror rotation angle is about ±55◦ , then the input polarization is rotated by 90◦ and exits the PMB parallel to its bend plane. For other mirror rotation angles, the output polarization is not purely linear but contains a small elliptical component. If the PMB did not change the horizontal input polarization, then the polarization incident at the last miter bend would also be horizontal. However, the PMMB only responds to the electric field that is parallel to its bend plane. Hence the required polarization at the location of this miter bend must be vertical. To establish that condition, the PMB mirror rotation angle was set to −54.7◦ . Fig. 6 shows the outputs of the WR6 detectors connected to the PMMB for a 240-s pulse with about 350 kW of 170 GHz incident power. A WR6 attenuator set to 19.5 dB attenuation was located before the WR6 detector for the forward coupled power, whereas no attenuator was in the path to the WR6 detector for the reverse coupled power. While the detectors were not calibrated, they were from the same lot and typically have similar sensitivities. Hence, from Fig. 6 it can be concluded that the directivity of the PMMB is
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Fig. 3. Steady-state ANSYS results for the calorimetric miter bend of Fig. 2, assuming 2600 W total room temperature absorption on a C18150 copper chromium zirconium mirror with 0.6 l/s flow. The mirror surface is colored, and the z-axis is along the major axis of the heated elliptical region. (a) Temperature distribution on mirror surface; (b) deformation of mirror surface.
greater than 20 dB. The gradual drop in the signal during the pulse is correlated with a slight drop in the gyrotron power. To measure the power absorbed in a mirror, the difference T in the input and output mirror cooling water temperatures in degrees C is multiplied by the flow F in liters per second and the heat capacity of water near room temperature: Pabs = 4184 F T watts
(1)
The water temperatures were measured with resistance temperature detectors (RTDs) inserted into the cooling lines through Swagelok® tee fittings. The flow meter was a vortex type. The data labeled absorbed power in the following figures actually is just the data calculated by Eq. (1), normalized to the input power. The input power was determined from calorimetric measurements at the dummy load. Generally more than 100 s was required for the data calculated by Eq. (1) to reach steady state. The power absorbed in the PMB mirror for a −54.7◦ mirror rotation angle is shown in Fig. 7 for a 240-s pulse test of the PMMB and for a 400-s pulse test of the CMB. The indicated absorbed power
(0.54%) is virtually identical for the two cases. Note that the power absorbed in the PMB mirror is much higher than the room temperature theoretical value (0.23%). In general, the theoretical and measured power absorbed in this mirror increased with increased mirror rotation angle. When the mirror rotation angle was 0◦ , the measured power absorbed in the PMB mirror was just a few percent higher than the room temperature theoretical value (0.124%). Calculations of the theoretical power absorption in the PMB mirror were based on space harmonic field calculations [13]. In previous tests in 2010, the power absorbed in the PMB mirror did not reach steady state when the incident power was about 600 kW and the mirror rotation angle was more than about 50◦ . Since the PMB mirror is well isolated from the polarizer housing, this result indicated that there might be a thermal runaway situation. The water flow was about 12 l/min for those tests. In the present tests, the water flow was restricted to only 9 l/min. Hence for the tests described in this paper, the power level was lowered to about 350 kW. For 1 MW operation with arbitrary mirror rotation angles, greater water flow will be required. In addition, a newer
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Fig. 4. Test line with long-pulse high-power 170 GHz gyrotron at the Japan Atomic Energy Agency fusion research facility in Naka. The PMMB and CMB power monitor miter bends were tested separately at the location indicated.
Fig. 5. PMMB power monitor installed in the test line of Fig. 4.
Fig. 6. Signals from the WR6 diode detectors on the forward (top curve) and reverse (lower curve) coupled ports of the PMMB. A WR6 attenuator set for 19.5 dB attenuation was placed before the detector of the forward coupled power. No attenuator was placed before the detector of reverse coupled power. The 170 GHz input power was approximately 350 kW.
design of the polarizer mirrors provides greater radial cooling than is possible in the polarizers used in these tests. The absorbed power in the PMMB and CMB are compared in Fig. 8 for the same case as in Fig. 7, which shows the power absorbed in the polarizer (PMB). The vertical axis is labeled as the fractional absorbed power, in accordance with Eq. (1). The theoretical room temperature absorption is only 0.08% for a copper mirror in this case, where the incident electric field is perpendicular to the plane of the PMMB or CMB bends. (The theoretical absorption is only slightly higher for the CuCrZr mirror in the PMMB.) The water temperature rise for the CMB reaches a steady state, because the mirror in that bend is well isolated from the miter bend housing, just as the mirror in the polarizer miter bend is well isolated from its miter bend housing. However, in the PMMB the water temperature rise never approaches a steady state. The mirror in the PMMB is directly connected to the miter bend housing. Hence power absorbed in the housing or nearby waveguides could be conducted to the mirror. In particular, the 2-m waveguide between the closest waveguide switch and the PMMB became anomalously hot during these tests. An explanation for this high waveguide heating is discussed separately [14] in terms of mode conversion caused by powerdependent misalignments. Even if such anomalous heating existed in a CW transmission line, all waveguides in such a line will be
Fig. 7. Power absorbed in polarizer miter bend when polarizer mirror rotation angle was set for −54.7◦ for tests of the PMMB and CMB power monitor miter bends. The longer pulse was for the CMB test. The line marked “Theory” is the calculated room temperature absorption on the polarizer mirror for an ideal grooved surface.
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Acknowledgments This work was supported by General Atomics Internal Research and Development funding. The high-power tests reported here were performed at the Japan Atomic Energy Agency (JAEA) at Naka, Japan. The authors gratefully acknowledge the assistance of Koji Takahashi, Keishi Sakamoto and the other JAEA staff who worked long hours each day to help complete the measurements. The reliability of the JAEA 170 GHz gyrotron was essential. Appendix A. Estimate of mode conversion loss due to distortion of miter bend mirror
Fig. 8. Power absorbed in PMMB and CMB mirrors when the polarizer mirror was set as in Fig. 7. The line marked “Theory” is the calculated room temperature absorption on a flat mirror with an ideal smooth surface when the incident electric field is perpendicular to the plane of the miter bend.
Assume the situation with the HE11 mode in a miter bend can be modeled approximately with an equivalent Gaussian beam. The best approximation of a Gaussian to an HE11 mode is with a beam radius of w = 0.32D,
(A1)
where D is the waveguide diameter. For a simple miter bend, the radius of curvature Ri of the equivalent Gaussian beam incident on the mirror is infinite. That is, its phase front is planar. Next, assume that the distorted mirror can be modeled as a portion of an ellipsoidal surface, as shown in Fig. A1. This figure shows a concave distortion, but a convex distortion should give a similar result. The dashed lines show the incident and reflected rays in the plane of the miter bend. For incidence at 45◦ as in a miter bend, the ellipsoidal surface can be described as follows Z2 X2 + Y 2 + 2 =1 B2 A Fig. 9. Fractional power absorbed on CMB mirror as a function of the polarizer mirror rotation angle.
cooled. That cooling will prevent excessive heat from reaching adjacent miter bend mirrors. Notice in Fig. 8 that the steady state indication of absorbed power in the CMB is only a little higher than the theoretical value. The results with a total of 11 different settings of the PMB mirror rotation angle are summarized in Fig. 9. The theoretical roomtemperature absorbed power in Fig. 9 is determined from Eq. (B7) of Appendix B and the theoretical polarization parameters corresponding to the PMB mirror rotation angles. An additional curve 20% higher than the room temperature values has been added; this curve fits the data reasonably well. Since the bulk resistivity of a copper mirror is approximately proportional to the absolute temperature, the surface resistance and hence the local absorbed power should be approximately proportional to the square root of the local absolute temperature. For ◦ example, a 100 ◦ C temperature rise from 27 ◦ C (300 K) should cause the absorbed power to increase by a factor of 400/300 = 1.155, corresponding to a 15.5% increase.
where √ A = 2B.
(A3)
where Z is measured along the axis of rotation of the ellipsoid, in the plane of the miter bend. X is also in the plane of the bend, and Y is perpendicular to the plane of the bend. The dimension E is equal to the square root of 2 times the waveguide diameter D. At the edge of the miter bend mirror in the Y = 0 plane, we have from Eq. (A2) and Fig. A1
2
B−ı B2
+
(0.5E)2 = 1. A2
(A4)
√ Using Eq. (A3) and E = 2D, we find from Eq. (A4) after neglecting the term in the square of the deflection that A=
D2 √ 4 2ı
(A5)
At the edge of the mirror in the X–Y plane at Z = 0, we must have X = B − ı, and Y = D/2. A simple calculation using Eqs. (A3) and (A5) verifies that Eq. (A2) is satisfied in this case. Hence the ellipsoidal
5. Conclusions High-power long-pulse tests as well as thermomechanical analyses indicated that the miter bends described in this paper are suitable for monitors of power in transmission lines similar to those planned for ITER. One miter bend (“power monitor miter bend” or PMMB) is suitable for rapid response to changes of both forward power and stray reflected power. The other miter bend (“calorimetric miter bend” or CMB) can accurately measure absolute power in long pulses. A single point calibration of the CMB against a dummy load can be useful; otherwise, only knowledge of the incident polarization is required for the measurement.
(A2)
Fig. A1. Geometry of deformed mirror surface.
J. Doane et al. / Fusion Engineering and Design 93 (2015) 1–8
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surface outlined here is a reasonable model of a miter bend mirror with deflection ı at its center. Noting that the focal length of the ellipsoidal surface described above is f = A/2 [15], we can now use the simple focal length formula 1 1 1 + = Ri Rr f
(A6)
where Ri and Rr are the radii of curvature of the incident and reflected beam, respectively, to find that Rr =
A D2 = √ , 2 8 2ı
(A7)
since Ri is infinite. The efficiency of coupling between two Gaussian beams with normalized amplitudes u1 (x,y) and u2 (x,y) is
2 ∞ 2 2 = u1 • u∗2 = d rdru1 u∗2 0
Fig. B1. Coordinate systems near mirror.
(A8)
0
At the miter bend mirror, the equivalent beams have the same beam radius and differ only in the radii of curvature. Let ui and ur represent the beams incident and reflected from the miter bend mirror, respectively. At the mirror we can write:
ui ∼exp and
−r 2 w2
ur ∼exp −r 2
(A9a)
1 w2
+j
Rr
Carrying out the integration in Eq. (A8), we find
=
1+
w2 2Rr
2 −1
∼ =
1−
w2 2Rr
2 (A10)
Inserting Eqs. (A1) and (A7) into Eq. (A10) and assuming that the deflection is much smaller than a wavelength , we find
2
∼ = 1 − 3.3
ı
(A11)
Since the mode conversion loss MCL is 1 − , the loss is
2
MCL ∼ = 3.3
ı
Fig. B2. Definition of polarization.
(A9b)
(A12)
A similar result was obtained by Michael Shapiro using analysis similar to that developed elsewhere [16]. For example, if the deflection is 0.04 mm at 170 GHz where the wavelength is 1.763 mm, MCL is 0.0017, or 0.17%. This is less than the mode conversion in an ideal miter bend with a flat mirror, which is 0.26% at 170 GHz in 63.5-mm waveguide. Appendix B. Theoretical dependence on input polarization of power absorbed on a miter bend mirror First let us define two coordinate systems as follows. Let the ˆ in the ϕ direction be perpendicular to the plane of unit vector ϕ ˆ where kˆ is the unit incidence, and define the unit vector ˆ as ϕ ˆ × k, vector in the propagation direction. Further, relative to the polarizer mirror define a right-handed coordinate system (ˆx, yˆ , zˆ ) where zˆ is ˆ is in the vertical direction normal to the mirror surface, and yˆ = ϕ perpendicular to the plane of incidence. See Fig. B1. Letting zˆ point away the mirror, then in terms of the incidence angle , ˆ = xˆ cos + zˆ sin.
Next we write the polarization incident on the mirror in terms of a polarization ellipse. The orientation of its major axis is rotated from ˆ clockwise by an angle ˛ (looking along the propagation ˆ and it has an ellipticity ˇ defined as the tangent of direction k), the ratio of the minor to major axes of the ellipse. See Fig. B2. The domains of these angles are 0 ≤ ˛ < 180◦ , and −45◦ ≤ ˇ ≤ 45◦ . With spatial and time dependence exp [j(ωt − k )] assumed, where is distance along the propagation direction, we can write the incident electric field components apart from a constant amplitude as: e = cos˛cosˇ + jsin˛sinˇ
(B1a)
eϕ = sin˛cosˇ − jcos˛sinˇ
(B1b)
Similarly, since the incident power flow is in the kˆ direction, we then have Z0 h = sin˛cosˇ + jcos˛sinˇ = −eϕ
(B2a)
Z0 hϕ = cos˛ cosˇ + jsin˛ sinˇ = −e
(B2b)
Then in terms of the (ˆx, yˆ , zˆ ) coordinates h = xˆ h cos + yˆ hϕ + zˆ h sin
(B3)
The surface current density on the mirror is equal to the total tangential magnetic field on the mirror, which is double the tangential component of the incident magnetic field. In terms of the incident magnetic field given by Eq. (B3) and the unit vector normal to the mirror surface nˆ = zˆ , the current density is J = 2nˆ × h = −2ˆxhϕ − 2ˆyh cos
(B4)
The fractional power ohmic loss on the mirror surface can be calculated by integration of the surface current over the mirror as follows:
PL =
Rs /2
| J|2 dA
Pi Acos
,
(B5)
8
J. Doane et al. / Fusion Engineering and Design 93 (2015) 1–8
where Pi is the incident power, is the angle of incidence, and Rs is the mirror surface resistance. From Eqs. (B2) and (B4), the squared current is
|J|2 = 4/Z02
1 − sin2 cos2 ˇsin2 ˛ + sin2 ˇcos2 ˛
(B6)
The incident power is Pi = (1/2)e × h, which from Eqs. (B2) is equal to 1/(2Z0 ). Hence the fractional loss is PL = 4
R [1 − sin2 (cos2 ˇsin2 ˛ + sin2 ˇcos2 ˛)] s Z0
cos
(B7)
In particular, if the incident electric field is linearly polarized in the plane of incidence (“E-plane” case) so that ˛ = ˇ = 0◦ then the term in square brackets in Eq. (B6) is unity. The magnetic field in that case is perpendicular to the plane of incidence and hence parallel to the mirror, so that all the incident field contributes to current on the mirror. If the incident electric field is linearly polarized perpendicular to the plane of incident (“H-plane” case), then ˛ = 90◦ , and the same sum is only cos2 . For = 45◦ as in a miter bend, then this sum is only 0.5. This result corresponds to the fact that some of the incident magnetic field is perpendicular to the mirror and hence does not contribute to the current. Eq. (B7) reduces to the familiar results 4(Rs /Z0 )/cos and 4(Rs /Z0 )cos for the E-plane and H-plane cases, respectively. The term 4(Rs /Z0 ) is simply the fractional loss on a flat mirror at normal incidence. For a circularly polarized input ˇ = 45◦ , and so for a typical miter bend with = 45◦ , the fractional loss is 4(Rs /Z0 )(1.06). In terms of the bulk resistivity and the free space wavelength , the surface resistance is
Rs =
Z0
(B8)
The effective surface resistance can be increased by surface roughness. References [1] J.L. Doane, R.A. Olstad, Transmission line technology for electron cyclotron heating, Fusion Sci. Technol. 53 (2008) 39–53 (Fig. 5). The first power monitor of this type was designed by Charles Moeller of General Atomics.
[2] V.I. Malygin, V.I. Belousov, A.V. Chirkov, G.G. Denisov, M.Yu. Shmelyov, I.V. Kurbatov, I.V. Kazanskiy, E.A. Solujanova, E.M. Tai, Transmission lines for microwave radiation of powerful continuous wave gyrotrons, in: Proc. 29th Int’l. Conf. Infrared and Millimeter Waves, Sept. 27–Oct., 2004, Institute of Electrical and Electronics Engineers, Karlsruhe, Germany, 2004, pp. 221–222. [3] V. Erckmann, et al., Electron cyclotron heating for W7-X: physics and technology, Fusion Sci. Technol. 52 (2007) p291ff. [4] C. Moeller, M. Cengher, Y. Gorelov, J. Lohr, Power and mode diagnostics for 110 GHz, in: National Gyrotron/ECH Technology Workshop, 26–27 Jan, 2011, San Diego, California, 2011. [5] J. Shi, W. Kasparek, A grating coupler for in-situ alignment of a Gaussian beam—principle, design, and low-power test, IEEE Trans. Antennas Propag. 52 (2004) 2517–2524. [6] L. Empacher, W. Förster, G. Gantenbein, W. Kasparek, H. Kumric, G.A. Müller, P.G. Schüller, K. Schwörer, D. Wagner, New developments and tests of high power transmission components for ECRH on ASDEX upgrade and W7-AS, in: Proc. 20th Int. Conf,. Infrared and Millimeter, Waves, Orlando, Florida, 1995, pp. 473–474. [7] J. Ruiz, W. Kasparek, C. Lechte, B. Plaum, H. Idei, Numerical and experimental investigation of a 5-port mitre-bend directional coupler for mode analysis in corrugated waveguides, J. Infrared, Millimeter, Terahertz Waves 33 (2012) 491–504. [8] W. Kasparek, D. Arz, L. Empacher, V. Erckmann, G. Gantenbein, F. Hollman, P.G. Schüller, K. Schwörer, M. Weissgerber, Performance of the 140 GHz prototype transmission system for ECRH on the stellarator W7-X, Fusion Eng. Des. 56–57 (2001) 621–626. [9] Reported in M.A. Henderson, “Miter Bend test programme,” draft of unpublished memo, 19 Feb. 2007, based on measurements at the University of Stuttgart on equipment described in W. Kasparek, A. Fernandez, F. Hollman, and R. Wacker, “Measurements of Ohmic Losses of Metallic Reflectors at 140 GHz Using a 3-Mirror Resonator Technique,” Int. J. Infrared Millimeter Waves, 22, (2001) 1695-1706. [10] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690 (Section 4.20; Fig. 3). [11] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690, Fig. 6. [12] M. Li, S.J. Zinkle, Physical and mechanical properties of copper and copper alloys, Compre. Nucl. Mater. 4 (2012) 667–690. [13] John Doane, Howard Grunloh, Ward Martin, Wen Wu, “Polarizer miter bends for high-power microwave transmission: ohmic loss and cooling,” in preparation for publication. [14] P. Anderson, et al., Recent component development at GA for ITER ECH transmission lines, in: US-EU-Japan RF Heating Technology Workshop, September 2014, Sedona, AZ, 2014. [15] P.F. Goldsmith, Quasioptical Systems, IEEE Press, Piscataway, NJ, 1998, pp. 109–110 (for example). [16] E. Kowalski, M.A. Shapiro, R.J. Temkin, Simple correctors for elimination of highorder modes in corrugated waveguide transmission lines, IEEE Trans. Plasma Sci. 42 (2014) 29–37 (Sections V and VI).