H. Idei

K. "Ohkubo

M. Sato

S. Kubo

T. Shimozuma

T." Watari

Y. Takita

National Institute for Fusion Science (NIFS-Repository)

§5. Radiation of Hybrid Mode from a Circular · Corrugated Waveguides Ohkubo, K., Kubo, S., Idei, H., Sato, M., Shimozuma, T., Takita, Y., Watari, T. Radiation of hybrid mode from a circular corrugated ( CC) waveguide are closely related with the coupling of hybrid mode with Gauss-Laguerre beam at the mouth. By using the mode matching method, we analyze propagation of the multi-Gauss-Laguerre beams equivalent to the HEn mode. We show evidence from the numer-ical calculations that radiation from two-, three-and multi-Gauss-Laguerre beams gives satisfac-tory approximation in both near- and far- field regions. The radiation pattern from multi-beam ~ 0 w 0 ~20 zC :IE < 0 -20 -10 0 10 ANGLE 8 (DEG) Figure 1: Radiation patterns of HEn obtained from (1) the single TEM00 mode, (2) two-beam approximation, ( 3) three-beam approximation, ( 4) multi-beam approximation and (5) Fresnel-Kirchhoff integral for (a) z= 100 m, (b) z= 1 m and (c) z=0.2 m is obtained from Gauss-quadrature integration with a relative in-certitude of 10-9 is adopted. In two- and three-beam superpositions, the summation of ( m = 0, 2) and ( m = 0, 2, 5) are carried out. In the LHD the transmission lines which consists of the ' CC-waveguide with 2a = 88.9mm for w/27r=84 and 168 GHz are being prepared. In coupling be-tween HEn and TEM0m for wo/a = 0.6436, the coefficient Am calculated. The TEMo2 mode has the largest value in first negative coupling coef-ficient group and the TEM05 mode has the max-imum value in second positive coupling group. In Fig.1 (a)- (c), radiation patterns for dif-ferent approximation at z = 100, 1 and 0.2 m are shown, respectively. With increasing su-perposition of higher modes in multi-beam ap-proximation, radiation pattern becomes close to that of Fresnel-Kirchhoff (FK) integral. The main beam of FK integral can be approximated well with two-beam (TEMoo + TEM02) or three-beam (TEM00 + TEMo2 + TEMos) superpos~­tions in near- and far- field regions. In the multi-beam by sum of TEMom up-to m = 20, ampli-tudes of higher order side-lobes agree well with that of FK integral. Arnplitudes of side-lobe Ey for z = 100 m are examined as a function of mmax· Near a bound-ary value m between positive and negative cou-pling coefficients, a new side-lobe appears. With increasing mmax, the amplitude of the side-lobe is saturated. The amplitude of side-lobes in two-and three-beam approximations is nearly equal to that of the multi-beam approximation with mmax := 2 and mmax = 5. The deviation c from the Fl( integral in single-, two-, three- and multi-beam superpositions with w0 / a = 0.6436 is cal-culated as a function of distance z, where the error c is defined by c == fIE x H*- EFK x H;,K121rrdr (2) f EFK X H;,K21rrdr For only far-field radiation, the single-beam ap-proxin1ation is slightly improved by changing w0 ja = 0.596 for 0.6436 as pointed out by Crenn [1]. In both near- and far-field radiations, two-beam and three-beam approximation is good with small c. The multi-beam approximation such as mmax = 20 are best. ~mma.x / _ /~mma.x lA l2 ( ) References Ey = Lm=O AmEyTEMom v Lm=O m . 1 [1] Rebuffi, S. and Crenn, J.P., International Journal of Infrared and Millimeter Waves, 10, Because the orthonormality in the waveguide 291-311, 1989. and free space is satisfied, the coefficient Am can be calculated. In the calculation, 35 points of 109 

Radiation of Hybrid Mode from a Circular Corrugated Waveguides

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