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Title: Correction of Distributed Optical Aberrations

Abstract

The objective of this project was to demonstrate the use of multiple distributed deformable mirrors (DMs) to improve the performance of optical systems with distributed aberrations. This concept is expected to provide dramatic improvement in the optical performance of systems in applications where the aberrations are distributed along the optical path or within the instrument itself. Our approach used multiple actuated DMs distributed to match the aberration distribution. The project developed the algorithms necessary to determine the required corrections and simulate the performance of these multiple DM systems.

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
902367
Report Number(s):
UCRL-TR-218949
TRN: US0702933
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION; ALGORITHMS; DISTRIBUTION; MIRRORS; OPTICAL SYSTEMS; PERFORMANCE

Citation Formats

Baker, K, Olivier, S, Carrano, C, and Phillion, D. Correction of Distributed Optical Aberrations. United States: N. p., 2006. Web. doi:10.2172/902367.
Baker, K, Olivier, S, Carrano, C, & Phillion, D. Correction of Distributed Optical Aberrations. United States. doi:10.2172/902367.
Baker, K, Olivier, S, Carrano, C, and Phillion, D. Sun . "Correction of Distributed Optical Aberrations". United States. doi:10.2172/902367. https://www.osti.gov/servlets/purl/902367.
@article{osti_902367,
title = {Correction of Distributed Optical Aberrations},
author = {Baker, K and Olivier, S and Carrano, C and Phillion, D},
abstractNote = {The objective of this project was to demonstrate the use of multiple distributed deformable mirrors (DMs) to improve the performance of optical systems with distributed aberrations. This concept is expected to provide dramatic improvement in the optical performance of systems in applications where the aberrations are distributed along the optical path or within the instrument itself. Our approach used multiple actuated DMs distributed to match the aberration distribution. The project developed the algorithms necessary to determine the required corrections and simulate the performance of these multiple DM systems.},
doi = {10.2172/902367},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Feb 12 00:00:00 EST 2006},
month = {Sun Feb 12 00:00:00 EST 2006}
}

Technical Report:

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  • The leakage fields of the extremities of the magnetic deflectors can be taken into account by defining an effective length d on the mean trajectory. In a magnet with pole pieces sufficiently large, the imaginary magnetic fronts of entry and outlet are planar in the useful zone because d is constant. However, the narrowing of the pole pieces causes the deformation of this front. in the case where the magnetic fronts are planar and normal to the direction of the mean trajectory, the magnetic fronts are curved and possess at each point two equal and opposed curvatures. Their section bymore » the median plane of the air gap is a convex curve towards the exterior. One can correct this curvature by giving to the mechanical face an equal and opposite curvature; the approximation obtained with the aid of plane faces is sufficient. When the correction of the aberration of the second order necessitates the use of curved mechanical faces, the parasite effect must be considered in the of the CERN, the double curvature of the face leads to troublesome aberrations much stronger than the abberrations of the second order. In the ease where the mechanical faces are inclined by an angle alpha /sub o/ on the direction of the same trajectory ("vertical" focusing), the magnetic fronts have a weaker average inclination. The "drag" DELTA alpha increases very rapidly with alpha /sub o/, and causes a distortion of the magnetic faces. The correcectors, and for a given magnet a method of correction can generally be perfected for all used values of alpha /sub 0/. (trauth)« less
  • This milestone has been accomplished. The Heavy Ion Fusion Science Virtual National Laboratory has completed simulations of a fast correction scheme to compensate for chromatic and time-dependent defocusing effects in the transport of ion beams to the target plane in the NDCX-1 facility. Physics specifications for implementation in NDCX-1 and NDCX-2 have been established. This milestone has been accomplished. The Heavy Ion Fusion Science Virtual National Laboratory has completed simulations of a fast correction scheme to compensate for chromatic and time-dependent defocusing effects in the transport of ion beams to the target plane in the NDCX-1 facility. Physics specifications formore » implementation in NDCX-1 and NDCX-2 have been established. Focal spot differences at the target plane between the compressed and uncompressed regions of the beam pulse have been modeled and measured on NDCX-1. Time-dependent focusing and energy sweep from the induction bunching module are seen to increase the compressed pulse spot size at the target plane by factors of two or more, with corresponding scaled reduction in the peak intensity and fluence on target. A time-varying beam envelope correction lens has been suggested to remove the time-varying aberration. An Einzel (axisymmetric electric) lens system has been analyzed and optimized for general transport lines, and as a candidate correction element for NDCX-1. Attainable high-voltage holdoff and temporal variations of the lens driving waveform are seen to effect significant changes on the beam envelope angle over the duration of interest, thus confirming the utility of such an element on NDCX-1. Modeling of the beam dynamics in NDCX-1 was performed using a time-dependent (slice) envelope code and with the 3-D, self-consistent, particle-in-cell code WARP. Proof of concept was established with the slice envelope model such that the spread in beam waist positions relative to the target plane can be minimized with a carefully designed Einzel lens waveform and transport line. WARP simulations have verified the efficacy of the Einzel lens while including more detailed beam physics. WARP simulations have also indicated some unpredicted transittime effects, and methods are currently being explored to compensate and reduce this complication. We have explored the use of an Einzel lens, or system of Einzel lenses, to compensate for chromatic aberrations in the beam focal spot in the NDCX-2 target plane. The final beam manipulations in NDCX-2 (linear velocity ramp, charge neutralization, high field final focus solenoid) are similar to NDCX-1 though the NDCX-2 beam has much higher energy and current. The most relevant distinctions are that the pulse duration at the entrance to the drift compression section is tenfold shorter, and that the beam energy tenfold higher, than in NDCX-1. Placing a time-dependent, envelope angle correcting element at the neutralized drift region entrance presents a very significant challenge to voltage holdoff and voltage swing V(t) in a single Einzel lens. Placing the Einzel lens(es) further upstream reduces the required voltage risetime V'(t) to effect the necessary envelope correction, while increasing the duration over which the timedependent voltage must vary. While this simplifies the technological challenge of designing and operating a Einzel lens in NDCX-2, it does require much finer control of the correcting waveform and measurements of its effect on space-charge dominated beams over a much longer axial path length to target than in the NDCX-1.« less
  • Nearly all designs of accelerators for heavy ion fusion rely on a velocity (energy) ramp to compress the beam longitudinally from its length in the accelerator to the length required at the target. The size of the velocity ramp is constrained by the longitudinal emittance of the beam. For example, if the longitudinal emittance is 0.05 eV {center_dot} s and we wish to produce a pulse having a width of {+-}2.5 ns at the target, we must supply an energy tilt such that the energy spread at the target is at least {+-}0.05 eV {center_dot} s/2.5 ns = {+-}2 xmore » 10{sup 7} eV. The minimal value of energy spread occurs when the beam has propagated to the point where there is no correlation between the time and energy variables of the beam particles. (In the simple approximation where the boundary of the longitudinal phase space containing the particles is an ellipse, the ellipse is erect at this point, i.e., not tilted with respect to the axes.) In any case, the energy spread can affect focusing. If, for example, the beam kinetic energy is of the order of 5 GeV, a tilt of {+-}2 x 10{sup 7} eV corresponds to a fractional energy spread of 0.004 and it may be possible to focus the beam to the required spot size without using an achromatic optical system. Nevertheless, an optical system that allows larger longitudinal emittance should lead to a less expensive accelerator since the tolerances on acceleration waveforms could be relaxed. Moreover, at lower kinetic energies the problem becomes more serious. If the kinetic energy of our example beam were 1 GeV rather than 5 GeV, the fractional energy spread would be 0.02. This much energy spread would likely produce serious chromatic aberrations leading to an unwanted increase in focal spot size. It is interesting to note that the lower limit on energy spread at the target does not depend on whether the beam is neutralized as it approaches the target. If the beam is not neutralized, it will require a larger initial velocity tilt to overcome longitudinal space-charge forces; but these forces will remove part of the tilt as the beam compresses. Al Maschke suggested that it is possible to reduce the chromatic aberrations by applying a time-dependent transverse focusing correction to the beam upstream of the final focusing lenses [1]. At this point, because of the energy tilt, there is a correlation between longitudinal position in the beam and particle energy. In other words, the average beam energy at the tail of the beam is larger than the average beam energy at the head of the beam. If the beam is completely neutralized as it drifts toward the final focusing lenses, the kinetic energies of the individual particles will remain nearly unchanged during compression. In this case, it is possible, in principle, to apply some 'pre-focusing' to the higher energy particles (those nearer to the tail of the beam) to compensate for their weaker focusing in the final lenses. Although kinetic energies of individual particles are not conserved if the beam is not neutralized, one still expects a positive correlation between the particle energies at the beginning of compression and at the end of compression so correction is still assumed to be possible. It is important that the pulse duration is larger upstream than it is at the final focusing lenses. Larger pulse duration makes it easier, from an engineering standpoint, to supply the power needed to drive the pulsed correction elements. Nevertheless, it still appears impossible or very costly to provide the needed power for some specific cases that have been studied. In the remainder of this paper we ignore this issue and try to determine if there are other fundamental limitations on how well one might correct. We conclude that there are other important limitations.« less