Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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Ion and Hall Thruster Plumes 427 d= b db d sin d = d d. d Compute the differential and total cross sections for (i) collisions between hard spheres of diameter d and (ii) a repulsive force field between particles that varies as k/ r2 (k is a constant). 4. The most general elastic collision process between two particles of unequal masses, m1 and m2, velocity vectors before the collision, u1 and u2, and after the collision, u1' and u2', can be represented by the geometrical construction in Fig. 8-21 using the following definitions: Relative velocities: U = u1–u2, U' = u1'–u2' Center-of-mass (CM) velocity: uc = (m1u1 + m2u2)/(m1 + m2) Reduced mass: M = m1m2/(m1 + m2) a. In the case of equal masses, m1 = m2 = m, and one stationary particle, u2 = 0, draw the new geometrical construction. What is the relationship between the scattering angle in the CM frame, , and the scattering angle in the laboratory frame, ? b. Convert the CM differential cross section, d/dCM, into the laboratory frame of reference, d/dL. m1u’1 m1u1 β m2u’2 MU’ MU θ m2u2 m1u1 + m2u2 = (m1 + m2) uc Fig. 8-21. Center of mass depiction of an elastic scattering event.

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