## Abstract

A procedure for determining the optimal design of an elliptical cavity is presented. Coupling between a cylindrical source and target is considered including the effects of finite source dimensions, radiation blocking by the source envelope, and reflective losses. It is found that the arc length should be at least 20 times the source envelope radius to achieve maximum efficiencies for a system with high reflectivity. A practical reflector is designed for a 100-kW continuous high-pressure argon arc that achieves an irradiance of 1.6 kW/cm2 on a 20-cm long target cylinder.

© 1984 Optical Society of America

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### Figures (8)

Fig. 1

Cross section of an elliptical cylinder.

Fig. 2

Comparison to theoretical channel model of experimental arc profile used in numerical calculations.

Fig. 3

Cross section of the 100-kW arc.

Fig. 4

Effects of finite length L where 2A is the separation of source and target, Re is the reflectivity of the end reflectors, ηe is the ratio of coupling efficiency for length L to that for infionite length.

Fig. 5

Maximum coupling efficiency for reflectivity of unity and a large diameter almost circular ellipse.

Fig. 6

Reduction of efficiency due to source blocking using unity reflectivity and an ellipse with A ~ BF.

Fig. 7

Overall efficiency where the reflectivity of both the ellipse and end reflectors Re = 0.9, F = 3 cm, SBR = 1.1 cm, Rs = 0.55 cm, L = 20 cm.

Fig. 8

Irradiance and overall efficiency for a system with P = 400 W cm−3 sr−1, Re = 0.9, Rs = 0.55 cm, L = 20 cm, SBR = 1.1 cm, f = 3 cm, and A = 11 cm.

### Equations (13)

$R = A cos ϕ i ^ + B sin ϕ j ^ , d R = ( - A sin ϕ i ^ + B cos ϕ j ^ ) d ϕ , d s = ∣ d R ∣ = ( A 2 sin 2 ϕ + B 2 cos 2 ϕ ) 1 / 2 d ϕ ,$
$F = ( A 2 - B 2 ) 1 / 2 ; N · I ^ s = N · I ^ t = - B ; ∣ I s ∣ = A - F cos ϕ ; ∣ I t ∣ = A + F cos ϕ ; d s = ∣ N ∣ d ϕ .$
$d Ω = sin ∝ d θ d ∝ , d H = - ( N ^ · D ^ s ) P d ∣ D s ∣ d θ d s sin ∝ d ∝ d l .$
$d W = - 2 ( N ^ · D ^ s ) P d ∣ D s ∣ d θ d s .$
$∫ P d ∣ D s ∣ = 2 P 0 ( R s 2 - ∣ I s ∣ 2 sin 2 θ ) 1 / 2$
$N ^ · D ^ s = cos ( β + θ ) = - cos β cos θ + sin β sin θ .$
$W = 4 P 0 ∫ - θ max + θ max cos β cos θ ( R s 2 - ∣ I s ∣ 2 sin 2 θ ) 1 / 2 d θ d s ,$
$W = 4 P 0 ∫ ( R s 2 / ∣ I s ∣ ) [ Z ( 1 - Z ) + sin - 1 Z ] cos β d s ,$
$W = 4 P 0 ∫ ( R s 2 B / ∣ I s ∣ ) [ Z ( 1 - Z ) + sin - 1 Z ] d ϕ .$
$F / A < ( R t - R s ) / ( R t = R s ) .$
$W = 4 P 0 ∫ ( 2 B Z R s 2 / ∣ I s ∣ 2 ) d ϕ , W = 4 P 0 R s 2 π R t .$
$η e = cos ∝ 1 + ∑ N = 1 ∞ R e N ( cos ∝ N + 1 - cos ∝ N ) ,$
$η e ′ = ( 1 + R e ) ∑ N = 0 ∞ R e N ( cos ∝ N + 1 - cos ∝ N ) / 2$