Microwave Emission from Flaring Magnetic Loops

Abstract

We discuss the microwave emission from a flaring loop (Spicer 1977). In particular we examine the following question: What will be the characteristics of the radio emission at centimeter wavelengths from a small compact flaring loop (average plasma density ne ≃ 1010 cm−3, average magnetic field at the footpoint of the loop Bℓ ≃ 500 gauss and Bt ≃ 100 gauss at the top of the loop and length of the loop, L = 109 cm), when the mechanism which pumps magnetic energy into the plasma in the form of heating and/or electron acceleration satisfies the following conditions. a. The magnetic energy is released in a small volume, (the energy release volume (ERV)), compared to the volume of the loop, and the rate at which magnetic energy is transformed into plasma energy is faster than the energy losses from the same volume. This causes a local enhancement of the temperature by as much as one or two orders of magnitude above the coronal temperature. b). The bulk of the energy released goes into heating the plasma and heats primarily the electrons (Te > Ti). Using these two assumptions one can easily show (Brown, Melrose and Spicer 1979, Vlahos and Papadopoulos 1979) that the high energy electrons in the tail of the velocity distribution in the ERV will instantaneously run away from this volume, and the resulting charge imbalance between the ERV and its surroundings (which still have average coronal temperatures ~ 106 K), will drive a return current, with velocity VD. When VD reaches the value of the local sound speed Cs ≃ 107 cm/sec low frequency ion acoustic waves will be excited at the interface of the ERV and its surroundings. It has been shown that the heat flow along the magnetic field lines is greatly reduced due to the presence of ion-acoustic turbulence (cf. Manheimer 1977). The bulk of the electrons in the ERV have electron-wave collision times **τw << 10–100 sec, longer than the impulsive phase of the flare. But since τw ~ v3 for those electrons with velocity v > ve (see Rudakov and Korablev 1966) the electrons in the tail will not “see” the ion sound waves and will stream freely towards the chromosphere.