1.7. CAVITY RESONANCES IN PARTICLE ACCELERATORS |
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Figure 1.9: Three meshes for the car length cut
The fourth eigenfunction of the acoustic vibration problem is displayed in Fig. 1.10. The physical meaning of the function value is the di erence of the pressure at a given location to the normal pressure. Large amplitudes thus means that the corresponding noise is very much noticable.
1.7Cavity resonances in particle accelerators
The Maxwell equations in vacuum are given by |
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curl E(x, t) = − |
∂B |
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(x, t), |
(Faraday’s law) |
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∂t |
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curl H(x, t) = |
∂D |
(x, t) + j(x, t), |
(Maxwell–Amp`ere law) |
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∂t |
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div D(x, t) = ρ(x, t), |
(Gauss’s law) |
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div B(x, t) = 0. |
(Gauss’s law – magnetic) |
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where E is the electric field intensity, D is the electric flux density, H is the magnetic field intensity, B is the magnetic flux density, j is the electric current density, and ρ is the electric charge density. Often the “optical” problem is analyzed, i.e. the situation when the cavity is not driven (cold mode), hence j and ρ are assumed to vanish.
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CHAPTER 1. INTRODUCTION |
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Figure 1.10: Fourth eigenmode of the acoustic vibration problem