Read e-book online Free Electron Lasers PDF

By S. Varro

ISBN-10: 9535102796

ISBN-13: 9789535102793

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Extra resources for Free Electron Lasers

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As a result, the bunch tail oscillates with respect to the head forming in the (z, x ) and in the (z, y) plane a characteristic “banana shape” [56]. Persistence of the slice oscillations along the linac and their amplification may cause the conversion of the bunch length into the transverse Design and Simulation Challenges of a Linac-Based Free Electron Laser in Presence of Collective Effects Design and Simulation Challenges of athe Linac-Based Free Electron Laser in the Presence of Collective Effects 49 11 dimension (beam break up).

S. s. contains the convolution of the transverse wake function with the local current distribution and is also linearly proportional to the relative displacement of the particle from the axis of the accelerating structure [54, 55]: 1 ∂ γ(σ) ∂σ (σ) ∂ x (σ, γ) + κ (σ)2 x (σ, γ) = γ(σ) ∂σ ζ −in f ty (19) w1n (ζ − ζ ) F (ζ ) [ x (σ, ζ ) − dc (σ)] dζ where σ = s/L is the distance from the linac entrance normalized with the total linac length L; ζ = z/lb is the longitudinal bunch coordinate at location σ measured after the arrival of the bunch head, normalized with the full width bunch length; F (ζ ) = I (ζ )/I pk is the local current normalized with the maximum peak current along the bunch; κ = kL is the average normalized focusing strength k integrated along the linac length L; w1n (ζ ) is the transverse wake function normalized with the wake amplitude; dc is the transverse offset of the beam respect to the linac axis.

8 can be modified with additional terms whose dependence on z is a polynomial. In such cases, the wake amplitude and the polynomial coefficients are determined by fitting procedures (see [46] as an example). 2 Energy loss The longitudinal wake potential induces a total energy loss of the electron beam so that the relative energy change at the bunch length coordinate z¯ is [17]: δw (z¯ ) = − e2 L γmc2 ∞ 0 w(z)n(z¯ − z)dz (9) ∞ where n(z¯ − z) is the longitudinal particle distribution with normalization −∞ n(z)dz = N (N is the total number of electrons in the bunch).

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Free Electron Lasers by S. Varro

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