Transcription of Chapter 2 Motion of Charged Particles in Fields
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Chapter 2 Motion of Charged Particles in Fields
Chapter 2 Motion of Charged Particles in Fields Plasmas are complicated because motions of electrons and ions are determined by the electric and magnetic Fields but also change the Fields by the currents they carry. For now we shall ignore the second part of the problem and assume that Fields are Prescribed. Even so, calculating the Motion of a Charged particle can be quite hard. Equation of Motion : dv m = q ( E + vB ) ( ) dt charge E field velocity B field Rate of change of momentum Lorentz Force Have to solve this differential equation, to get position r and velocity (v= r ) given E(r, t), B(r, t). Approach: Start simple, gradually generalize. Uniform B field, E = 0. mv = qv B ( ) Qualitatively in the plane perpendicular to B: Accel. is perp to v so particle moves in a circle whose radius rL is such as to satisfy 2 vrL is the angular (velocity) frequency mrL 2 = m = q v B ( ) | |1st equality shows 2 = v2 L 2/r (rL = v / ) 17 Figure : Circular orbit in uniform magnetic field.
Even so, calculating the motion of a charged particle can be quite hard. Equation of motion: dv m = q ( E + v B ) (2.1) dt charge Efield velocity ∧ Bfield Rate of change of momentum Lorentz Force Have to solve this differential equation, to get position r …
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