[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

They are described by their remanent field b r in

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range. They are described by their remanent field B r in Teslas which for SmCo pure permanent magnets (PPM) reaches 0.85 T while for NdFeB ones 1.17 T. The period of these IDs called λ 0 is the separation between identical magnetic structure units in the s direction. The main IDs are: the wavelength shifter, the multipole wiggler, and the undulator. We will only present here the wiggler and the undulator, which are the most frequently used IDs. Wigglers Wigglers are assemblies of alternative magnetic field regions which induce fairly large deviations of the electrons from the straight trajectory. These
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70 A. Simionovici and J. Chavanne Period l 0 Gap e - Vacuum chamber Magnet blocks e - Fig. 2.29. Scheme of the magnetic structure in an insertion device segment of period λ 0 multipole devices act on the e -beam as a succession of BM which generate photons incoherently. The total intensity generated by N poles spaced by λ 0 is equal to that of 2 N bending magnets (a period comprises two bends in the e -beam trajectory which generate X-rays). The vertical magnetic field inside a wiggler (end-effects neglected) is, to a good approximation, a sine wave of period λ 0 : B Z = B 0 × sin(2 πs/λ 0 ) and B 0 = 1 . 43 × B r × e ( πg/λ 0 ) (2.15) with B r the remanent magnetic field in T and g the gap in cm, while the transverse velocity in the horizontal plane is v X /c = 0 . 3 E (GeV) B Z ( s )d s = K γ cos(2 πs/λ 0 ) , (2.16) where distances are in m and B in T. K is the dimensionless deflection para- meter which governs the regime of the ID: K = 93 . 4 B 0 ( T ) λ 0 ( m ) . (2.17) For K < 1 values, photons are emitted in a cone smaller than 1 and they interfere, yielding the “undulator” case. For K 1, virtually no interference occurs and the emitted flux can be obtained summing up the contributions of the trajectory points tangent to the emitted cones. Undulators Undulators (Fig. 2.30) are thus “multipole” wigglers of small K values and a large number of poles. Due to the small (but frequent) trajectory deviations, the flux can be collected from the whole trajectory and due to interference
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2 X-Ray Sources 71 1.65 m Fig. 2.30. ESRF undulator carriage effects it is proportional to N 2 ( N = number of poles). The wavelength of the spectrum emitted by an undulator is the Fourier transform of its time structure and thus exhibits a line spectrum corresponding to the periodicity of the emission in the time domain and is given by: λ = λ 0 2 2 (1 + K 2 2 + γ 2 θ 2 ) , i = 1 , 2 , 3 , . . . , (2.18) where i is the harmonic number and θ the observation angle in the horizontal plane. The fundamental wavelength is then: E fund = 0 . 949 E 2 [GeV] λ 0 [cm] (1 + K 2 2 + γ 2 θ 2 ) . (2.19) The odd harmonics are the ones of maximum yield and their flux is given by: I (phot / s / 0 . 1%bw) = 1 . 43 × 10 14 NI [ A ] Q i , (2.20) where Q i is a function of the harmonic number i : Q i = iK 2 ( 1 + K 2 2 ) J ( i 1) / 2 iK 2 4 + 2 K 2 J ( i +1) / 2 iK 2 4 + 2 K 2 2 (2.21) and J the standard Bessel function.
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72 A. Simionovici and J. Chavanne 2.4.4 SRW Package When addressing the SR fundamentals, it is more straightforward to treat the matter from the point of view of a user not particularly familiar with
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  • Spring '14
  • MichaelDudley

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