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Quasilinear Theory with Spontaneous Emission

Quasilinear Theory with Spontaneous Emission. An Important Concept. Cyclotron resonance is not an efficient process. Only a narrow spectrum of waves can interact with the beam particles. Resonant Interaction. k. The purpose of introducing the concept of spontaneous emission is two fold:.

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Quasilinear Theory with Spontaneous Emission

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  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.

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