#### DMCA

## Excitation of a Rectangular Electromagnetic Cavity by a Passing, Relativistic Electron

### Cached

### Download Links

### Citations

22 |
Electromagnetic Theory for Microwaves and Optoelectronics,
- Zhang, Li
- 2008
(Show Context)
Citation Context ...ty may be characterized as transverse electric (TE) or transverse magnetic (TM) as described, for example, in sec. 8.7 of [7]. The field patterns of a few of the lowest modes are sketched below (from =-=[8]-=-). The lowest mode, TM010, for a cavity of radius R, withthez-axis being that of the cavity, has fields in cylindrical coordinates (r, φ, z), where the resonant frequency is Ez = E0 J0(kr) e −iωt , (3... |

10 |
Electromagnetic Radiation
- Milton, Schwinger
- 2006
(Show Context)
Citation Context ... electron is Eex = 32πe kdxdydz ∣ sin kxx sin kyy sin kdz 2 ∣ = 32e √ d2 x + d2 ∣ y dz sin kxx sin kyy sin kdz . (22) 2 ∣ This problem has been considered by a very different approach in sec. 14.2 of =-=[3]-=-, 2 for the particular case that dx = dy ≡ a = λ/ √ 2anddz ≡ b = λ/2, with x = y = a/2 √ 2. For this case, eq. (22) gives Eex =64e/λ 2 , and the energy of this excitation is (recalling eq. (17)) Uex =... |

5 |
Experimental investigations on geometrical resolution of optical transition radiation (OTR), Nucl
- Artru
- 1998
(Show Context)
Citation Context ... there is only a power-law falloff at larger angles, and the optical transition radiation from an intense beam of charged particles can be used to measure the spot size to accuracy of a few optical λ =-=[5, 6]-=-. 6The energy stored in the TM010 mode of a cavity of axial length L is ∫ 2 2 ∫ 2 |E| + |B| |E| U = dVol = 16π 8π dVol = E2 0L 4 = E2 0LR2J 2 1 (kR) 8 ∫ R 0 J 2 0 (kr) rdr = E2 0 LR2 4 ∫ 1 J 0 2 0 (k... |

5 |
et al., Beam Profile Measurement at 30 GeV Using Optical Transition Radiation
- Catravas
(Show Context)
Citation Context ... there is only a power-law falloff at larger angles, and the optical transition radiation from an intense beam of charged particles can be used to measure the spot size to accuracy of a few optical λ =-=[5, 6]-=-. 6The energy stored in the TM010 mode of a cavity of axial length L is ∫ 2 2 ∫ 2 |E| + |B| |E| U = dVol = 16π 8π dVol = E2 0L 4 = E2 0LR2J 2 1 (kR) 8 ∫ R 0 J 2 0 (kr) rdr = E2 0 LR2 4 ∫ 1 J 0 2 0 (k... |

5 |
et al., Accelerator design concept for future neutrino facilities, 2009
- Apollonio
(Show Context)
Citation Context ...bunch are small compared to the wavelength of a mode, then the excitations of the various electrons add coherently. As an example (taken from the accelerating cavities of a so-called neutrino factory =-=[13]-=-), we consider a bunch of n =10 12 muons passing through a right circular cavity with L =30cm, R =15cm, for which the excitation of the fundamental mode, with kR = kL/2 =2.405, hasEex ≈ 5.4 × 10 5 V/m... |

3 | A Maxwellian Perspective on Particle Acceleration
- Zolotorev, Chattopadhyay, et al.
(Show Context)
Citation Context ...tially unchanged if v ≈ c. Then, the energy gained by the electron is equal and opposite to the change in the electromagnetic field energy of the cavity due to the additional excitation of the cavity =-=[1]-=-. From this, we can deduce the strength of the excitation due to the electron. Our argument is a kind of reciprocity relation: the energy of excitation of a mode of a cavity by an electron is related ... |

1 |
Wake Potenitals of a Relativistic Current in a Cavity, Part
- Weiland, Zotter
- 1981
(Show Context)
Citation Context ...R) kL sin ∣ 2 ∣ = 12.3eJ0(kr) LR kL sin , (38) ∣ 2 ∣ noting that J1(2.405) = 0.519. The excitation of cylindrical cavities has been extensively considered for particle accelerators. See, for example, =-=[10, 11]-=-, which uses a Green-function method due to Condon [12] (that appears to be very similar to the method of Schwinger [3]). Equation (38) is, I believe, the same as eq. (A8) (in SI units) of [10] with p... |

1 |
Electronic Generation of Electromagnetic Oscillations
- Condon
- 1940
(Show Context)
Citation Context ... that J1(2.405) = 0.519. The excitation of cylindrical cavities has been extensively considered for particle accelerators. See, for example, [10, 11], which uses a Green-function method due to Condon =-=[12]-=- (that appears to be very similar to the method of Schwinger [3]). Equation (38) is, I believe, the same as eq. (A8) (in SI units) of [10] with p =0, g = L, r =0and ct > g; i.e., fortimes after the ch... |