Coherent Smith-Purcell Radiation Generated by Tilted Grating
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Coherent Smith-Purcell Radiation Generated by Tilted GratingA.P. Potylitsyn, L.G. SukhikhTomsk Polytechnic University, Tomsk, Russia
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OverviewIntroductionSmith-Purcell Radiation
theoretical formalism for a tilted grating
Smith-Purcell Radiation from a grating infinite in transverse direction
Smith-Purcell Radiation from a finite grating
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INTRODUCTION
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Smith-Purcell Radiation
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~0.2ps ~1ps
Coherent Radiation from a train of bunches
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Spectrum of Frequency Locked Coherent Radiation
Radiation line width is proportional to Nb-1
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Smith-Purcell radiation gain due to several microbunches
Parameter ValueElectron energy, Ee
10 MeV
Grating period, d 300 umNumber of strips, N 101
Impact-parameter, h 1 mm
Observation angle,
90 degree
Microbunch length, 0
# of microbunches, Nb
On the figure
Distance between microbunches, rf
300 um
Smith-Purcell radiation spectrum
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Possible Issue In the case of frequency-locked coherent
radiation a spacing between radiation lines in the spectrum strongly depends on the microbunch spacing. Parameter Value
Electron energy, Ee
10 MeV
Microbunch length, 0
# of microbunches, Nb
1
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One may need a way to adjust the SPR wavelength to actual microbunch spacing
1. One can change observation angle 2. One can change grating period d
Tilt the grating
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Tilted grating For the first time was calculated by P. Karataev et
al.
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SMITH-PURCELL RADIATION THEORETICAL FORMALISM FOR A TILTED GRATING
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AssumptionsThe grating under consideration
is an infinitely-thin one with vacuum gaps.
The grating material is an ideal conductor.
Calculations are made for using single electron approach
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Smith-Purcell radiation modelRadiation field
Symbol Meaning
r0Observer
coordinates
n Normal to the grating surface
E0 Electron field
g Free space Green function
Ssc
Grating surface (sum of all
strips)
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Infinite grating vs. finite gratingIn the case of infinite grating (in
transverse direction) and far-field zone one can obtain nice analytical solution of the problem.
In the case of finite grating one needs to perform numerical double integration but this case is closer to real life. In this case one can also take into account the finite distance between the grating and the detector.
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SPR FROM THE INFINITE GRATING
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Theoretical model
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Theoretical modelThe integration can be carried out
analytically, over all grating strips resulting in the following radiation field:
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Calculation parametersParameter Value
Electron energy, Ee 10 MeVGrating period, d 300 umNumber of strips, N 21Impact-parameter, h 1 mmObservation angle, 90 degMicrobunch length, 0# of microbunches, Nb 1
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Example of Line Shift
Radiation is polarized in xz plane
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Line Position
Radiation is polarized in xz plane
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Line Width
Line width=∆ 𝜆𝜆1𝑁
Radiation is polarized in xz plane
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SPR FROM THE FINITE GRATING
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Theoretical modelIn the case of finite grating one
needs to carry out numerical integration of the equation
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Calculation parametersParameter Value
Electron energy, Ee 10 MeVGrating period, d 300 umGrating width 15 mmNumber of strips, N 21Impact-parameter, h 1 mmObservation angle, 90 degMicrobunch length, 0# of microbunches, Nb 1
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Grating – detector distance
Parameter Infinite grating Finite grating (R = 300 mm)
Line position 300.7 um 300.5 umLine width 4.03% 4.06%
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Line shift
Radiation is polarized in xz plane
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Line position
Radiation is polarized in xz plane
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Line width
Radiation is polarized in xz plane
Line width=∆ 𝜆𝜆1𝑁
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ConclusionTilt of the grating changes the
SPR line position. This effect may be used for radiation spectrum adjustment or beam diagnostics.
There are some differences between infinite grating model and finite grating model that are not really understood now.
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THANK YOU FOR YOUR ATTENTION