Fast Electrons, Bremsstrahlung, and Bowling

The electrons accelerated in solar flares have very high velocities. A 30 keV electron has a speed of about 100000 km per second, one-third the speed of light! The highest energy electrons accelerated in many flares travel at nearly the speed of light. The theory of relativity and many years of observing fast particles have shown that a particle's velocity can become arbitrarily close to the speed of light as its energy increases, but it cannot reach or exceed the speed of light.

Bowling Alley ImageThe interaction of a fast electron with a plasma has a lot in common with bowling. When a bowler rolls the ball down the alley, he increases the ball's velocity and therefore accelerates it. The ball's energy also increases. Despite the high velocity of the electrons accelerated in flares, the bowling ball carries much more energy than the electron because of the tiny mass of the electron compared to that of the ball. The sum of the energies of all of the electrons accelerated in a flare is much greater than the energy of the bowling ball, however. The interpretation of observations of the hard x-ray emission from flares has in fact suggested that all of the energy released in flares initially goes into accelerated electrons! It is difficult to see how this could happen. Nevertheless, the energy in accelerated electrons is substantial and it is important for us to determine how much of the flare energy does go into these energetic particles.

Bowling Ball and Pins ImageWhen the bowling ball hits the pins, it loses some of its energy to knocking over the pins. When an accelerated electron streams through the thermal plasma, it loses its energy to collisions with the thermal electrons: the plasma electrons are heated. Since the bowling ball only has up to 10 pins to collide with, it usually retains some of its energy after the collisions and loses the rest of it to the back wall of the alley. The accelerated electrons will continue to stream through the plasma until they lose most of their energy and become part of the thermal plasma. Electrons traveling downward toward the surface of the Sun that do not lose all of their nonthermal energy in the corona will lose it in the much denser chromospheric plasma below the corona.

When the bowling ball hits and knocks over the pins, a loud crash is heard. This is because the air around the ball and pins is disturbed and the disturbance radiates outward as a sound wave. A small fraction of the energy given to the ball by the bowler has been converted to waves. When an energetic electron streams through a plasma, its collisions with the charged particles that make up the plasma disturbs the electric and magnetic fields associated with it, producing electromagnetic radiation. The radiation from interactions with the heavy ions (primarily protons) is much greater than from interactions with the plasma electrons (imagine that, like the plasma protons, about half the bowling pins are roughly 2000 times heavier than the ball). These are the bremsstrahlung x-rays observed from solar flares. The energy radiated as bremsstrahlung is typically 100000 times smaller than the energy lost to the plasma electrons.

The thermal electrons in a plasma also interact with the plasma ions, producing thermal bremsstrahlung. This thermal radiation provides a way to study the hot plasma produced in flares, just as the nonthermal bremsstrahlung provides a way to study the accelerated electrons. The energy lost to thermal bremsstrahlung will eventually cool a hot plasma, but other cooling mechanisms such as conduction are often more important.

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