Download Free-Electron Lasers in the Ultraviolet and X-Ray Regime: by Peter Schmüser, Martin Dohlus, Jörg Rossbach, Christopher PDF
By Peter Schmüser, Martin Dohlus, Jörg Rossbach, Christopher Behrens
The major target of the booklet is to supply a scientific and didactic method of the physics and know-how of free-electron lasers. a number of figures are used for illustrating the underlying principles and ideas and hyperlinks to different fields of physics are supplied. After an advent to undulator radiation and the low-gain FEL, the one-dimensional thought of the high-gain FEL is constructed in a scientific approach. specific emphasis is wear explaining and justifying many of the assumptions and approximations which are had to receive the differential and imperative equations governing the FEL dynamics. Analytical and numerical ideas are provided and demanding FEL parameters are outlined, reminiscent of achieve size, FEL bandwidth and saturation strength. probably the most vital good points of a high-gain FEL, the formation of microbunches, is studied at size. the rise of achieve size because of beam power unfold, area cost forces, and three-d results equivalent to betatron oscillations and optical diffraction is analyzed. The mechanism of Self-Amplified Spontaneous Emission is defined theoretically and illustrated with various experimental effects. numerous equipment of FEL seeding by means of coherent exterior radiation are brought, including experimental effects. The world’s first delicate X-ray FEL, the consumer facility FLASH at DESY, is defined in a few aspect to offer an impact of the complexity of such an accelerator-based gentle resource. The final bankruptcy is dedicated to the recent difficult X-ray FELs which generate tremendous excessive radiation within the Angstrøm regime. The appendices comprise supplementary fabric and extra concerned calculations.
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Extra resources for Free-Electron Lasers in the Ultraviolet and X-Ray Regime: Physical Principles, Experimental Results, Technical Realization
Example text
10) with a complex amplitude E˜ x (z) which will be a function of the path length z in the undulator. The initial phase ψ0 is put to zero, see the previous section. The phase of the amplitude E˜ x (z) may vary with z which means that the phase velocity of the FEL light wave may differ slightly from the phase velocity c of an electromagnetic wave. This effect will be studied in Chap. 6. Inserting Eq. 10) into the wave equation yields ⎡ ∂ ˜jx . 11) 2 i kΦ E˜ x√ (z) + E˜ x√√ (z) exp[i(kΦ z − ωΦ t)] = μ0 ∂t To proceed further we make the slowly varying amplitude (SVA) approximation in order to get rid of the second derivative E˜ x√√ .
7 and Sect. 1. 27) 2π S(ψ) sin(k ψ)dψ . 0 Defining the complex Fourier coefficients ck = ak − ibk one can rewrite S(ψ) in the form ∞ c0 +≈ S(ψ) = ck exp(i k ψ) . 28) 2 k=1 The complex Fourier coefficients are given by ck = 1 π 2π S(ψ) exp(−i k ψ)dψ . 29) 0 In order to find the relation between the Fourier coefficients and the current density we look first at the dc current density which is proportional to the zeroth Fourier coefficient c0 /2 ∝ a0 /2 = N/(2π). From j0 = −e c ne and ne = N/(Ab λΦ ) follows then 2π c0 .
This can be seen as follows. Since we have ignored the longitudinal oscillation, the longitudinal coordinate and the longitudinal momentum of the electron are zero in the moving system z∗ = 0 , pz∗ = 0 . Then the Lorentz transformations of time and electron energy read t = γ¯ t ∗ , W = γ¯ W ∗ , so the radiation power in the laboratory system becomes P=− dW ∗ dW = − ∗ = P∗ . dt dt The undulator radiation power per electron in the laboratory system is therefore 18 2 Undulator Radiation Fig. 9 c. The undulator parameter is K = 1.