Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Discovery
- 3 Basic theory
- 4 Observations of masers
- 5 Maser molecules
- 6 Environments of masers
- 7 Advanced theory
- 8 Computer modelling
- 9 Masers as diagnostics
- 10 Future prospects
- Appendix A Boltzmann's formula
- Appendix B Vector identities
- Appendix C Dirac delta-function
- Appendix D Change of variables in integration
- Appendix E Coordinate systems
- Appendix F Lagrange inversion theorem
- Appendix G Local standard of rest
- Appendix H Stochastic processes
- Appendix I Fourier transforms
- Appendix J Matrices
- Appendix K The centre of mass frame
- Appendix L Quantum-mechanical operators
- References
- Index
Appendix H - Stochastic processes
Published online by Cambridge University Press: 05 May 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Discovery
- 3 Basic theory
- 4 Observations of masers
- 5 Maser molecules
- 6 Environments of masers
- 7 Advanced theory
- 8 Computer modelling
- 9 Masers as diagnostics
- 10 Future prospects
- Appendix A Boltzmann's formula
- Appendix B Vector identities
- Appendix C Dirac delta-function
- Appendix D Change of variables in integration
- Appendix E Coordinate systems
- Appendix F Lagrange inversion theorem
- Appendix G Local standard of rest
- Appendix H Stochastic processes
- Appendix I Fourier transforms
- Appendix J Matrices
- Appendix K The centre of mass frame
- Appendix L Quantum-mechanical operators
- References
- Index
Summary
Noise power
The theory of the noise voltage generated by a resistor was developed by Nyquist (1928), following experimental measurements by Johnson (1928). The phenomenon is therefore named after either, or both, of these researchers.
Suppose we have a long coaxial transmission line at temperature T. This line acts as a 1-D cavity for the propagation of electromagnetic waves at a velocity, v, where we will assume v ≃ c. We can then follow the analysis of Section 1.3.4 to obtain the number of available modes. If the transmission line is laid out along the z-axis, the electric and magnetic fields are restricted to the xy-plane, and boundary conditions require the electric field to be zero at the ends of the line, where z = 0 and z = L. Allowed modes along the transmission line are therefore restricted by a z-version of Eq. (1.33) to kz = πmz/L, for integer mz, and the 1-D nature of the problem implies that mz is the only such integer required to define a mode. There are still, however, two independent polarizations allowed (along the x- and y-axes), so we modify the above restriction on modes to k = 2πm/L, where we have dropped the z-subscript.
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- Maser Sources in Astrophysics , pp. 378 - 381Publisher: Cambridge University PressPrint publication year: 2012