The results of the stress relieving and tempering processes are dependent on the temperature and time of the process, which may be correlated using a parameter such as Holloman's (Holloman-Jaffe) parameter or the Larsen-Miller parameter. These parameters are a measure of the thermal effect of the process on the metallurgical transformation of the steel during tempering. The processes that exhibit the same tempering parameter are expected to exhibit the same effect (such as hardness). However, these more traditional numerical expressions assume isothermal tempering processes which seldom exist in production tempering ovens due to the heat-up period prior to soaking

Type III radio bursts are radio emissions associated with solar flares. They are considered to be caused by electron beams travelling from the solar corona to the solar wind. Magnetic reconnection is a possible accelerator of electron beams in the course of solar flares since it causes unstable distribution functions and density inhomogeneities (cavities). The properties of radio emission by electron beams in an inhomogeneous environment are still poorly understood. We capture the nonlinear kinetic plasma processes of the generation of beam-related radio emissions in inhomogeneous plasmas by utilizing fully kinetic particle-in-cell code numerical simulations. Our model takes into account initial electron velocity distribution functions (EVDFs) as they are supposed to be created by magnetic reconnection. We focus our analysis on low-density regions with strong magnetic fields. The assumed EVDFs allow two distinct mechanisms of radio wave emissions: plasma emission due to wave–wave interactions and so-called electron cyclotron maser emission (ECME) due to direct wave–particle interactions. We investigate the effects of density inhomogeneities on the conversion of free energy from the electron beams into the energy of electrostatic and electromagnetic waves via plasma emission and ECME, as well as the frequency shift of electron resonances caused by perpendicular gradients in the beam EVDFs. Our most important finding is that the number of harmonics of Langmuir waves increases due to the presence of density inhomogeneities. The additional harmonics of Langmuir waves are generated by a coalescence of beam-generated Langmuir waves and their harmonics.

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Magnetic reconnection can convert magnetic energy into kinetic energy of non-thermal electron beams. Those accelerated electrons can, in turn, cause radio emission in astrophysical plasma environments, such as solar flares via micro-instabilities. The properties of the electron velocity distribution functions (EVDFs) of those non-thermal beams generated by reconnection are, however, still not well understood, in particular, properties that are necessary conditions for some relevant micro-instabilities. We aim at characterizing the EVDFs generated in 3D magnetic reconnection by means of fully kinetic particle-in-cell code simulations. In particular, our goal is to identify the possible sources of free energy offered by the generated EVDFs and their dependence on the strength of the guide field. By applying a machine learning algorithm on the EVDFs, we find that (1) electron beams with positive gradients in their 1D parallel (to the local magnetic field direction) velocity distribution functions are generated in both diffusion region and separatrices. (2) Electron beams with positive gradients in their perpendicular (to the local magnetic field direction) velocity distribution functions are observed in the diffusion region and outflow region near the reconnection midplane. In particular, perpendicular crescent-shaped EVDFs (in the perpendicular velocity space) are mainly observed in the diffusion region. (3) As the guide field strength increases, the number of locations with EVDFs featuring a perpendicular source of free energy significantly decreases. The formation of non-thermal electron beams in the field-aligned direction is mainly due to magnetized and adiabatic electrons, while in the direction perpendicular to the local magnetic field, it is attributed to unmagnetized electrons.