1. Quasilinear Theory with Spontaneous Emission An Important Concept

2. Cyclotron resonance is not an efficient process Only a narrow spectrum of waves can interact with the beam particles.

3. Resonant Interaction k

4. The purpose of introducing the concept of spontaneous emission is two fold: The concept itself is important in plasma physics. Induced and spontaneous emissions of radiation are essential in radio astronomy. One should know that in quasilinear theory spontaneous emission of waves can be more important than “collisions”.

5. We must remember: Conceptually in plasmas particles and waves are inseparable. Particles are accelerated by absorbing wave energy. Then waves are emitted by accelerated particles. In a plasma in thermodynamic equilibrium the rate of wave absorption is equal to the rate of wave emission.

6. However, theoretically Our understanding of spontaneous radiation is limited to resonant emission. It is not known whether non-resonant quasilinear process can or cannot lead to spontaneous emission. It is a totally new topic area.

7. One may imagine: If the plasma deviates slightly from an equilibrium state, the two rates are no longer in equilibrium. For instance, a weak instability sets in and some “waves” gain energy. “In principle” the plasma may adjust itself so that a new equilibrium state is attained. But there is difficulty!

8. In Plasmas We may have spontaneous emission or induced emission. We can have induced absorption. But spontaneous absorption does not make sense (within the context of quasilinear or linear theory). That is why “heating” is difficult.

9. The Usual Quasilinear Theory Only considers induced emission of waves. In general it is desirable to include spontaneous emission in the theory. What does “spontaneous emission” mean.

10. Let us consider the wave kinetic equation. In the quasilinear theory discussed so far the wave kinetic equation take the form The growth rate may be conceived as an emission coefficient. The term on the right-hand side denotes “induced emission” of waves.

11. Theory includes spontaneous emission The wave kinetic equation becomes The last term represents spontaneous emission of waves. It is discussed in the literature. The meaning of “spontaneous is clear.

12. Let us consider the case of Landau damping If the plasma is in thermodynamic equilibrium and the plasma is in a stationary state, we expect The following relation is anticipated The emissivity depends on temperature. The relation yields thermal fluctuations.

13. QLT with Spontaneous Emission

14. Astrophysical Radio Emission Intense radiation is mostly produced via induced processes rather than spontaneous processes. Spontaneous emission usually require large population of energetic electrons. On the other hand our understanding of induced emission process is still very limited.