Optical Measurements of Neutral Cesium Mass Flow Rate in Field Emission Thrusters

A = integral of the relative density profile, au A21 = Einstein coefficient for spontaneous emission, s 1 B21 = Einstein coefficient for stimulated absorption, s 1 C1 = calibration coefficient for the first moment I , m 3 s C2 = calibration coefficient for the second moment I , au c = speed of light, ms 1 dS = elementary surface element, m F = normalized velocity distribution function, m 3 s f = normalized projected velocity distribution function, m 1 s I = laser intensity, Wm 2 Ia = accelerator current, A Ie = emitter current, A ISat = saturation intensity, Wm 2 I = first moment of the fluorescence signal, s 2 I = second moment of the fluorescence signal, s 3 J = first moment of the transmission, s 1 K = cesium number density integrated along the absorption line of sight, m 2 kT = proportionality constant for thrust-dependent mass flow rate, mgh 1 N 1 LRef = length of the reference cell, m mCs = cesium atom mass, kg nCs = cesium number density, m 3 nRef = cesium number density in the reference cell, m 3 q = cesium mass flow rate, mgh 1 Q = quenching rate, s 1 S = fluorescence signal detected, count s 1 T = transmission coefficient u = microscopic velocity, ms 1 U = averaged velocity along a laser axis, ms 1 V = probed volume, m V = averaged velocity vector in the laboratory coordinate system, ms 1 Va = accelerator voltage, V Ve = emitter voltage, V V ij = averaged velocity along the Z axis, measured at node i; j , ms 1 Y = normalized line-shape function, s = deexcitation rate, s 1 0 = transition wavelength, m = frequency, MHz L = laser frequency, MHz = solid angle, sr