Sources Of Aberrations In The Optics For The Remote Steering ITER ECRH Upper Launcher A. Moro, A. Bruschi, P. Platania, C. Sozzi Istituto di Fisica del Plasma “Piero Caldirola” Euratom-ENEA-CNR Association via Cozzi 53 20125 Milan (Italy) Abstract. Quasi-optical systems designed and developed for the ECRH Upper Launcher in ITER need to be treated with particular attention, since reflection from generic surface introduces aberrations whose effects influence beam propagation. From an optical point of view the system has to maintain a sufficient steering capability and beam convergence in order to localize heating and current drive over a large range of plasma radii in ITER scenarios, limiting as much as possible aberration effects. Principal sources of aberrations in the optical systems of the Remote Steering (RS) ECRH Upper Launcher are reviewed in this work. In particular we analyze effects of double curvature mirrors in both single and multiple end mirror configurations for the RS option. Added to this, first order deformation effects on mirror reflecting profiles caused by thermal loads are included in the analysis. Email of A. Moro: firstname.lastname@example.org INTRODUCTION In this work we analyze different aspects of the optics for the Remote Steering (RS) design for the Upper Launcher in the ITER ECH&CD System. We include in the description of the EC launching systems those effects whose evaluation will be a necessary step in the optimization phase of the project. Effects of double curvature mirrors are studied and optimized for the single-end front mirror configuration for the RS Upper Launcher . Quasi-optical systems which use more than one mirror may give general astigmatism and general astigmatic gaussian beams emerge. The fundamental parameters of such beams and the laws of propagation are known in literature  and can be applied to the latest version of the RS dogleg option design under investigation . Among the sources of aberrations, deformation effects due to high thermal loads on mirrors may also be included. Their influence on beam propagation in terms of beam dimensions and directions are briefly discussed and an example of how they could be taken into account in the latest RS dogleg design is given. DOUBLE CURVATURE OPTIMIZATION FOR THE SINGLEEND MIRROR DESIGN Reflection of an astigmatic gaussian beam from generic surfaces is well described in literature (see for example ) and formulas to compute fundamental quantities are also available. Double curvature in constrained configurations may bring a gain since it opens the possibility to produce a whole range of output beams among which the best suited to the purpose can be chosen. As an advance with respect to the discussion on beam size evaluation, we considered the opportunity to use a double curvature front mirror in the Single-End Mirror (SEM) design previously developed . In its reference configuration 3 ports are used (with 8 beams per port, divided in two rows, an upper row and a lower one). One of the two curvatures, precisely the one measured in the intersection with the steering plane, is kept fixed with the value determined by the optimum trade-off between the output steering range requested and the resulting beam size, since large range and low dimensions are not compatible . The second principal curvature, orthogonal to the steering plane, can be opportunely chosen to reduce beam divergence after reflection due to self-diffraction. In the reference configuration studied, the nominal focal length of the original spherical mirror is f1=1125 mm and this value fixes the curvature in the steering plane of the new mirror. The curvature in the plane orthogonal to the steering one is the free parameter. In Fig.1 (left) different resulting beams after reflection are presented for different values of the ratio = R2/R1 (=1, =0.5, =0.25, =0.125 and =0.06) in the case of the zero-steering launching line, for an input gaussian beam with beam waist w0=12.5 mm at the waveguide aperture. FIGURE 1. Left: Beam spot sizes (mm) and astigmatic beam axes after reflection, for the lower row, zero-steering launch beam line. Curves represent different values of (from outer to inner: =1, =0.5, =0.25, =0.125 and =0.06). Right: Beam widths for single spherical mirror, single curvature and with double curvature as a function of the steering angle, for the lower row beam line. Beam widths of the resulting astigmatic beams have been evaluated at the reference optimization distance after the front mirror for this specific configuration , and presented in a plane orthogonal to the beam line given by the wave vector k. The spot ellipse new axes of astigmatism are shown and used to define its orientation angle with respect to a reference horizontal line. Being the resulting principal directions not in the tangential (nor in the sagittal) plane, they should be labeled as quasi-tangential and quasi-sagittal. We found that R2=525 mm (=0.086) gives the best improvement in the quasi-sagittal direction with respect to the original single (spherical) mirror setup. This improvement is different as we move on the steering plane from minimum (=-12) to maximum (=+12) steering angle and in the two resulting astigmatism directions as shown in Fig. 1 (right). Starting from a single curvature mirror, improvements from 5% to 25% in beam widths in the quasi-sagittal direction (depending on the steering angle) can be achieved. Single mirror setup is considered less preferable than the alternative dogleg option due to its high thermal loads on mirror, nevertheless the margin of improvement shown here, combined with increased input beam waist at the waveguide aperture, may give a total gain from 15% to 25%. GENERAL ASTIGMATIC GAUSSIAN BEAMS IN THE REMOTE STEERING DOGLEG OPTION General astigmatism can be found in complex non-orthogonal quasi-optical systems where more than one mirror is used. For these beams the constant intensity ellipse and the constant phase ellipse (or hyperbolas) are oriented at an angle with respect to each other. General astigmatic gaussian beams (GAGB) can be described adding a complex rotation angle to the set of beam parameters usually used to define the beam. Formally a GAGB corresponds to a conventional astigmatic gaussian beam rotated around its axis of propagation by a complex-valued angle =+i. FIGURE 2. Left: The dogleg setup. Right: Spot ellipse (mm) in a plane orthogonal to the output wave vector k (in-going) after the last front mirror (z=0) at relevant distance in plasma (z=ztar) for =0 steering: beam spots for different approximations are shown. The GAGB treatment best reproduces both beam size and orientation. The complex rotation angle is a fundamental parameter, since its real and imaginary parts are related to the real angles w and R, which describe the orientation of the constant intensity and constant phase curves with respect to the original coordinate systems. Astigmatism axes orientations are found to be function of the propagation distance z even in free space . Beam widths in the resulting astigmatism directions and spot ellipse orientation as a function of the propagation distance after the last front mirror have been evaluated with the GAGB formalism for the latest dogleg option setup (Fig. 2), in which two curved mirrors at oblique angles require such a general treatment , in order to improve the results obtained previously with approximated calculations with simple astigmatic beams (described in ref. ). Beam spots and beam patterns calculations performed with GRASP code  have been compared (Fig. 2, right). BEAM DEFORMATIONS AND DEVIATIONS A simple estimation of deformation effects on the output beams due to the large power density at the end mirrors can be done for a given cooling layout system once the deformed profile is known. Deformed surfaces are modeled with a change in the local mirror curvatures and can be considered as a sequence of two different elements, one defocusing (the bump) and one focusing (the un-deformed reflecting surface). We performed a calculation for the RS dogleg option in the worst case encountered in terms of deformation effects, where two beams overlap on the first mirror. In Fig. 3 (central) we present the evaluations of the deformation profiles along first mirror width (approximately directed along toroidal direction) and along first mirror length (approximately poloidally directed). Similar profiles were obtained for the second mirror where no beam overlapping occurs. FIGURE 3. Left: beam widths [mm] as a function of distance from the last mirror for quasi-toroidal and quasi-poloidal directions: when thermal deformations of M1 (with beam overlap) and M2 (no beam overlap) are included, wider beams in the quasi-toroidal direction are obtained. Center: deformation profiles caused by beam overlapping on the first mirror of the dogleg design examined. Profiles are smoother in the poloidal direction while present a steepening in the toroidal direction as a consequence of the cooling layout system. Right: Description of reflection on opposite sides of deformed mirrors when two beams overlap. Evaluation of deformation effects on the final output beam shows an increase in the beam width, which is found to be relevant only for the quasi-toroidal direction (one of the two principal directions of the beam width) while the beam width in the perpendicular direction (quasi-poloidal) is nearly unaffected (beam radius in the quasitoroidal direction can be twice larger the beam radius in case of un-deformed mirror at relevant distance in the plasma, as shown in Fig. 3, left). This is due to the fact that the curvature radii of the bump are RB1 -6.9 m and RB2 -27.8 m on M1 mirror (RB1 -6.0 m and RB2 -51.3 m on M2 mirror). Some effects are also expected on beam deviations with respect to the un-deformed surface. Although a single beam impinging on a deformed reflecting surface is not expected to undergo to axis deviations but only to negligible shift, possible deviations may occur for two beams impinging on different sides of the bump resulting form the merging of the two deformation spots (Fig. 3, right). The deviation is then evaluated taking into account the different normal vector n for reflection from different sides of the profile. The resulting beam deviations (0.1 in terms of output poloidal angle ) give a beam shift at relevant distance in the plasma of the order of a few mm. CONCLUSIONS Investigation of reflection from double curvature surfaces is necessary to have a description of the beams after generic or deformed mirrors in quasi-optical systems. A standard description with simple astigmatic beams may not be fully adequate whatever general astigmatism emerges. Additional effects are also found in real situations, when high power beams may give deformations effects that modify the focal properties of reflecting elements, possibly enhancing beam divergence and consequently lowering the control of the power deposition in the plasma. ACKNOWLEDGMENTS This work has been carried out in collaboration with a team of scientists from IFPCNR and European Laboratories as a part of the EFDA Task TW5-TPHE-ECHULB1 . REFERENCES 1. A. Bruschi et al., Advanced Optics for the Remote Steering ITER ECRH Upper Launcher, Journal of Physics: Conference Series 25 (2005), 112-119. 2. J.A. Arnaud, H. Kogelnik, Gaussian Light Beam with General Astigmatism, Appl. Opt., 8, 1687-1693 (1969). 3. D. M. S. Ronden et al., “Detailed design mm-wave system of the preferred option, including description of mmwave performance in terms on steering range, steering accuracy, beam dimensions vs steering angle, etc. at a level suitable for inclusion in the ITER reference CAD system”, EFDA Deliverable 2005 (a).5 & (a).9 4. C. A. Balanis, “Advanced Engineering Electromagnetics”, Wiley, 1989. 5. A. Moro, A. Bruschi, “Inclusion in the optimization of double curvature effects and general astigmatism. Deformation calculations based on the cooling layout for the dogleg option for the RS design”, EFDA Deliverable 2005 (a).7.1 . 6. P. Platania, C. Sozzi, “Patterns calculations for Dogleg configuration”, EFDA Deliverable 2005 (a).3.1 .