COMPUTER PHYSICS COMMUNICATIONS 1 (1970) 440-444. NORTH-HOLLAND PUBLISHING COMPANY

C-51

S P E C T R A L I N T E N S I T Y , A N G U L A R D I S T R I B U T I O N A N D P O L A R I S A T I O N

O F S Y N C H R O T R O N R A D I A T I O N F R O M A M O N O E N E R G E T I C E L E C T R O N

J a m e s LANG Department of Natural Philosophy, Tke Universi ty, Glasgow W2, Scotland

Received 17 September 1970

P R O G R A M S U M M A R Y

Title of program: SYNCHROTRON RADIATION

Catalogue number: ACQR

Computer f o r which the program is designed and others upon which it is operable

Computer: ICL KDF9. Installation: (1)Glasgow Universi ty, Glasgow W2, Scotland (2) Culham Laboratory, Abingdon, Berks . , England

Operating sy s t em or moni tor under which the program is executed: Egdon 3

Programming languages used: FORTRAN

High speed s tore required: 3000 words. No. of bits in a word: 48

Is the program overlaid? No

No. of magnetic tapes required: None

What other peripherals are used? Line P r in te r , Card Reader

No. of cards in combined program and tes t deck: 321

Keywords descr ip t ive o f problem and method of solution: Atomic, Solid State, Synchrotron, Radiation, Po la r i sa t ion , Angular Distr ibution, Intensity, Spectral Intensity, Absolute Intensity, Absolute Source, Radiomet ry , Re la t iv i s t - ic Electron, C i rcu la r Orbit , Besse l Function, Series Solution, Integration.

Nature of the physical problem The absolute power radiated by a re la t iv is t ic e lec-

tron t ravel l ing in a c i r cu l a r orbit in a synchrotron can be calculated theoret ica l ly . This p rogram evaluates , for an electron of specified energy and orbit radius , the power radiated round the orbit (a) as a function of wavelength (i.e. spec t ra l d i s t r ibu-

tions) (b) as a function of the angle above or below the orbi -

tal plane at any par t icu la r wavelength. These angu- lar d is t r ibut ions are given for the component po la r - ised with E - v e c t o r in a plane paral lel to the orbital plane and for the component polar ised with E - v e c - tor in a plane perpendicular to the orbital plane.

Method o f solution The ex p re s s io ns used in the calculat ions are those

given by Tomboulian and Har tman [1] and which were originally given by Schwinger [2] in a slightly different form. Olsen [3] and Wesffold [4] have shown how the angular distr ibution fo rmula also gives the po la r i sa - tion. The equations contain Besse l functions of the s e c - ond kind (McDonald functions) Kn(S) of o rder n which are calculated f rom s e r i e s expansions . The spec t ra l dis tr ibut ions involve the integrat ion of functions of or - der 5/3 and the other dis t r ibut ions involve the squar ing of functions of order 1/3 and 2/3.

Restr ic t ion on the complexi ty of the problem The s e r i e s method of solution of the Besse l funct ions

me a ns that the a rgument of Be s se l function is prevented f rom exceeding six. For the spec t ra l d i s t r ibu t ions the calculation is thus cut-off when the wavelength is 2.52 t imes down on the waveLength of peak power, the wave- lengths higher than that of the peak power being unaf- fected. For the angular d is t r ibu t ions at a fixed wave- length. The res t r i c t ion in t roduces a cut-off as the an- gle above or below the orbital plane is increased . How- ever . at this cut-off the power is down by at leas t two orders of magnitude on the power at the peak of the an- gular distr ibution.

Typical running t ime The tes t case compi les in 22 seconds and takes 77

seconds to run on the Glasgow Univers i ty KDF9.

References [1] D.H.Tomboul ian and P . L . H a r t m a n , Phys . Rev. 102

(1950) 1423. [2] J .Schwinger , Phys . Rev. 75 (1949) 1912. [3] H.Olsen , Kgl. Norske Videnskab. Selskabs Skrif ter

(1952) hr . 5. [4] K.C.West fo ld , A s t r o p h y s . J . 130 (1959) 241.