Simulating ohmic and mode conversion losses in corrugated waveguides for ITER LFSR system C. Lau, M.C. Kaufman, (ORNL) G.R. Hanson (U.S ITER) E.J. Doyle, W.A. Peebles, G. Wang (UCLA) D.W. Johnson, A. Zolfaghari (PPPL) and the LFSR team IRW 12 May 20, 2015 1 Managed by UT-Battelle
Outline of talk research and development to understand losses in circular corrugated waveguides for ITER ECH and LFSR corrugated waveguides discussion of simulation code, MORA, to predict ohmic losses and mode conversion losses from manufactured curvature, tilts, offsets, miter bends, gaps for arbitrary frequency, number of modes and waveguide corrugation dimensions quality assurance and validation tools in checking (and improving) MORA simulation and waveguide manufacturing technology preliminary simulation results for LFSR transmission line curvature, ohmic, miter bend, gap losses as a function of frequency 2 Managed by UT-Battelle unlike theory which does not depend on corrugation parameters, simulation shows the effect of corrugation parameters on losses loss estimates have increased, as more realism has been added to calculations comparison of simulation results to experimental results (experimental test stand) simulation of different corrugation parameters to accommodate expected LFSR frequency bandwidth and possible stray ECH protection
Mode conversion theory and simulations for corrugated waveguides Theory is well known for ohmic loss 1, mode conversion loss due to curvature 2, tilts 2, offsets 2, diameter 2, gaps 3, miter bends 3 curvature, tilt losses ~ (a/λ) 2, and are more significant at high frequencies miter bends, gaps losses ~ (λ/a) 3/2, and are more significant at low frequencies ORNL has developed simulation 4, MORA, to calculate losses for circular smooth and corrugated waveguides any linear combination of hybrid or LP modes can be used for inputs and outputs ohmic losses 1, curvature 2, offsets 2, tilts 2 are solved using mode coupling and propagation code miter bends 5, gaps 5 are solved using mode matching code beam deflection physics (gravity sag) Monte Carlo analysis, based on measurements of manufactured errors and tolerances, is used to generate sample transmission lines to estimate statistical nature of mode conversion errors 3 Managed by UT-Battelle 1. Nanni, J Infrared Terahz Waves (2012) 2 Doane, Infrared Millimeter Waves (1985) 3 Doane, Int. J. Electronics (1994) 4 Kaufman, ECH Technical Meeting (2014) 5 Shapiro, Fusion Sci. Tech. (2010)
Modelling curvature and ohmic losses solve the mode coupling and propagation equations: and are the curvature of the waveguide in the x and y directions. curvature can be manually or automatically inputted K mn is curvature coupling coefficients, α m is attenuation constant A standard Adams-Moulton predictor-corrector ODE solver is used to integrate the coupled equations. Large discontinuities in the curvature are handled by stopping and restarting the integration at the discontinuity Iteration with reduced tolerances to a specified convergence criterion (<0.1%) 4 Managed by UT-Battelle
Examples of Curvature sagging of waveguides due to gravitational loading misalignments in waveguide supports discrete tilts, offsets between waveguide sections 1-D ode can be solved analytically manufactured errors from extrusion and fabrication significant uncertainty (and possible loss) for ITER ECH transmission line currently 5 Managed by UT-Battelle
Modelling miter bends and gaps Linear combination of hybrid modes are propagated across either gap or miter bend diffraction and ohmic losses are calculated Gaps/miter bends are treated as large square cavity 1 cavity modes are matched at waveguide boundary with hybrid modes Miter bends additionally uses: method of images approach truncation at walls FFT and inverse FFT for each step across gap no reflection is included Sample gap drawing Kowalski, MIT libraries 2010 (a) Sample miter bend drawing (b) Miter bend (simplified from (c) ) (c) Miter bend under method of images 1 Shapiro, Fusion Sci. Tech. (2010) 6 Managed by UT-Battelle
Combining miter bends, gaps, tilts, manufacture curvature, ohmic losses into a simulation Waveguide deflection is modeled as sum of Fourier modes Each section of waveguide is rotated to match the previous section + any tilt angle. The sections are joined endto-end and then rotated so that both ends sit at zero displacement. miter bends, gaps are modules within code that occur between stopping and restarting of the Adams-Moulton predictorcorrector ODE solver 7 Managed by UT-Battelle
Modeling transmission line statistically Long runs of transmission line will have many free parameters: length of each of N support spans: relative height of each support: length of each of M waveguide sections: tilt error at each waveguide coupling: tilts at miter bend mirror profile of manufactured deflection for each piece of waveguide: Some are chosen depending on the simulation, but still may have associated errors Others are chosen from a distribution The Monte Carlo technique is appropriate for this modeling by running large number of simulations for each case 8 Managed by UT-Battelle
Code verification of MORA to literature Verify against analytic ohmic attenuation for miter bends and corrugated waveguides (Nanni, IFW2012) and analytic coupling coefficients of two different literature sources (Doane, IMW1985 and Li, IJE 1991) Verify against analytic double S-bend (Doane, white paper) Verify against analytic discrete tilt (Thumm, IEEE NPSS 2002) Verify against analytic two-mode constant curvature (Doane, IMW1985) Verify against analytic two-mode hyperbolic secant curvature (Doane, IMW1985) Verify against experimental PLT/PDX 90 H-bend (Doane, IEEE MTT 1984) Verify against constant curvature waveguide bend to COMSOL FEM smooth and corrugated wall, limited to low frequency, 1-4cm length Verify against simulated waveguide gap (Shapiro, FST 2010) Verify against simulated miter bend (Shapiro, FST 2010) Verify against waveguide gap to COMSOL FEM Smooth and corrugated wall, limited to 1-2.5 cm gap distances 9 Managed by UT-Battelle
Relating MORA to actual manufacturing parts Geometrical dimensioning and tolerances are being used to set tolerances inspection data has been gathered on some sample corrugated waveguides and miter bends based on machining tolerances some Monte Carlo inputs are based on these tolerances and data 10 Managed by UT-Battelle
Measuring straightness in manufactured waveguide Laser tracker was required to measure within long waveguides SMR sphere with bearings naturally recenter at bottom of tube. Waveguide is rotatable 11 Managed by UT-Battelle
Outline of this talk research and development to understand losses in circular corrugated waveguides for ITER ECH and LFSR corrugated waveguides discussion of simulation code, MORA, to predict ohmic losses and mode conversion losses from manufactured curvature, tilts, offsets, miter bends, gaps for arbitrary frequency, number of modes and waveguide corrugation dimensions quality assurance and validation tools in checking (and improving) MORA simulation and waveguide manufacturing technology preliminary simulation results for LFSR transmission line curvature, ohmic, miter bend, gap losses as a function of frequency 12 Managed by UT-Battelle unlike theory which does not depend on corrugation parameters, simulation shows the effect of corrugation parameters on losses loss calculations have increased, as more realism has been added to calculations comparison of simulation results to experimental results (experimental test stand) simulation of different corrugation parameters to accommodate expected LFSR frequency bandwidth and possible stray ECH protection
Results for LFSR manufactured curvature losses curvature losses are not that large due to expected straight waveguides likely acceptable loss for LFSR (unless > 170 GHz is desired) 50, 105, 170 GHz cases with LFSR groove parameters simulated (170 GHz shown) note that losses must be small (~< 10-20%), or else else mode purity is compromised 13 Managed by UT-Battelle
Results for LFSR ohmic losses Ohmic loss does increase substantially at low frequencies depends on corrugation parameters losses can be large but it does not affect mode purity analytical formula (that includes all waveguide surface areas) gives the same result for this 14 Managed by UT-Battelle
Results for LFSR miter bend diffraction losses this simulation is done for current ITER LFSR parameters as frequency is decreased, mode conversion loss rises dramatically and deviates from theory note that miter bend theory (Doane, 1994) assumes λ << a and d = λ/4 when approximations is not valid, HE 11 is no longer a very good Gaussian beam 15 Managed by UT-Battelle simulation is consistent with theory when theory is applicable
Results for JET: miter bend diffraction losses JET has 40 m long waveguide run with 9 miter bends No signal detected below 44 GHz, low signals at 44-50 GHz (Sirinelli, RSI 2010) 16 Managed by UT-Battelle suspected to be due to beam divergence and size of windows/mirrors miter bends probably play a factor as well JET waveguide run and corrugation dimensions provided by A. Sirinelli
Results for LFSR gap and aperture losses gap theory (Doane, 1994) also assumes λ << a and d = λ/4 5 and 25 mm gaps use for gap extension joints 200 mm gap simulates monostatic coupling of 100 mm to mirror simulation deviates strongly from theory for 5 mm gap, less so for 200 mm gap difference between gaussian beam and corrugated electric field for aperture coupling does not appear too significant (may check with FWR3D to make sure?) difference is large for small gaps, but total gap loss is small unless there are many of these 17 Managed by UT-Battelle
Comparison of MORA to experimental test stand Test stand is built mostly to test corrugated waveguide performance Low frequency testing mostly complete (33-50 GHz) miter bends and ohmic loss are most important loss mechanisms High frequency testing will start soon (110-165 GHz) Curvature, tilt effects will be understood here Current waveguides are not up to ITER ECH specs, but may be ok? for ITER LFSR 18 Managed by UT-Battelle
Comparison of MORA to experimental test stand - - MORA simulation simulation results only account for miter bend and ohmic loss only simulations is 1 amplitude of HE 11 mode mode purity for simulations do not appear to be significant issue experimental measurements compares favorably to MORA note that previous estimates implicitly assume d= λ/4, which are inconsistent with experimental results 19 Managed by UT-Battelle
Different corrugation parameters for ITER LFSR for 40 m, 10 miter bends Current miter bends optimized > 200 GHz only ohmic and miter bend losses included here (no Bragg scattering) Signal to noise may be a question on the lower frequency end? 20 Managed by UT-Battelle Stray ECH radiation is substantially less at low frequency end
Different corrugation parameters for ITER LFSR for 40 m, 10 miter bends Changing miter bend corrugations can improve losses at low frequency if dedicated low frequency waveguide is necessary high frequency operation will no longer be possible for this waveguide (Larger) diameter is unlikely given space constraints at front-end 21 Managed by UT-Battelle
Different corrugation parameters for ITER LFSR for 40 m, 10 miter bends ECH stray protection at 170 GHz Shutters, isolators, quasi-optical and waveguide filters are all possibilities optimization of corrugation parameters may also help as a ECH notch filter, as losses can be made surprisingly large 22 Managed by UT-Battelle
Different corrugation parameters for ITER LFSR for 40 m, 10 miter bends ECH stray protection to be effective as notch filter require high machining accuracy 23 Managed by UT-Battelle estimated 25 μm error on corrugation cutters multiple corrugation depths may help broaden (but lower) peak
Conclusion and Future Work MORA simulation has been developed to calculate losses in ITER ECH and LFSR transmission line preliminary results have been achieved showing simulated ohmic losses and mode conversion losses due to miter bends and curvature code has successfully been compared to many examples in literature and shows very good preliminary results to experimental measurements larger than expected (and more realistic) miter bend losses compared to theory is now included in our calculations of transmission line loss as transmission line layout becomes more clear, run Monte Carlo cases for the full transmission line guide and confirm further guide design depending on resources, experimental testing of different ITER LFSR corrugations may be necessary, especially if there is a desire to use LFSR transmission line for ECH stray protection 24 Managed by UT-Battelle
Pull-boring delivers much better straightness than the other sets of waveguide. But hasn t been corrugated. 25 Managed by UT-Battelle
Miter bend diffraction losses mode conversion losses at low frequencies go to a wide distribution of spurious modes (usually HE 1n ), many of which are quickly attenuated in waveguides and have large losses through miter bends mode purity is still high in simulations after multiple bends (>90%) even with relatively large miter bend losses implies that miters does not significantly affect mode purity and phase measurement 26 Managed by UT-Battelle
Varied parameters Results Ohmic attenuation factor Waveguide corrugation depth 35 GHz, 31 m, 10 miter bends 50 GHz 31 m, 10 miter bends 35 GHz, 15.5 m, 4 miter bends 50 GHz, 15.5 m, 4 miter bends Experiment 44-48% 22-27% 25-27% 11-16% 1 actual 48.2 22.6 22.1 12.0 2 actual 51.7 23.9 25.6 12.7 1 λ/4 33.8 19.0 16.0 8.6 2 λ/4 36.4 20.1 17.7 9.2 data from Doyle, IRW 2015 Simulations added in green line (attenuation factor of 1, actual corrugation depth, loss to HE11 for two way loss) 27 Managed by UT-Battelle Simulation smoothed to.5 GHz frequency bandwidth (similar to experiment)