Comparative study of the gyrotron, the free-electron laser, and the wiggler-free free-electron laser

The gyrotron, the free-electron laser, and the wiggler-free free-electron laser are compared. First, the flows in the three systems are examined in their steady state. Then the interaction of the electron beam with free-space electromagnetic waves is studied by using a fluid picture. The growth rate of the instability is found by calculating the nonreal roots of the three different dispersion relations. It is shown that at off-resonance the interactions in the gyrotron and in the wiggler-free free-electron laser are identical. However, at resonance, the instability in the gyrotron disappears, while the growth rate in the wiggler-free free-electron laser is maximal, as in the usual free-electron laser. The maximum growth rate in the wiggler-free free-electron laser scales as some small parameter to the power of (2/5, compared to the same small parameter to the power of (1/2 for the gyrotron, and to the power of (1/3 for the free-electron laser. Thus the wiggler-free free-electron laser, while having some resemblance to each of the two other systems, the gyrotron and the free-electron laser, is clearly different from both. In terms of gain, it has a higher gain than the gyrotron but lower than the free-electron laser.