helix modes are launched, since empty waveguide modes can only propagate above $2 {\,\rm GHz}$. These modes have electric field components along the helix axis  [@Dimonte]. Launched electromagnetic waves travel along the helix with the speed of light; their phase velocities, ${v_{\phi
j}}$, along the axis of the helix are smaller by approximately the tangent of the pitch angle, giving $2.8 \times10^6 {\,\rm m/s} <
{v_{\phi j}} < 5.3 \times10^6 {\,\rm m/s}$. Waves on the beamless helix are slightly damped, with $|{k_{j}^{0i}}|/|{k_{j}^{0r}}|
\approx 0.005$ where ${k^0 = k^{0r} + {\rm i\,} k^{0i}}$ is the beamless complex wave number. The dispersion relation closely resembles that of a finite radius, finite temperature plasma, but, unlike a plasma, the helix does not introduce appreciable noise. Finally the cumulative changes of the electron beam distribution are measured with the velocity analyzer, located at the end of the interaction region. This trochoidal analyzer [@guyomarc'h] works on the principle that electrons undergo an ${\bf E \times
B}$ drift when passing through a region in which an electric field ${\bf E}$ is perpendicular to a magnetic field ${\bf B}$. A small fraction (0.5%) of the electrons passes through a hole in the center of the front collector, 