Monday Week 2 Lecture Jeff Eldred 1 Monday Week 2 Lecture Jeff Eldred Relativistic Kinematics, Retarded Potentials, Synchrotron Radiation 1 1 1 1 1

Overview Relativistic Kinematics Part II: Retarded Time 2 Overview Relativistic Kinematics Example of Neutrino Beams Part II: Retarded Time Retarded Time Potential from a moving point charge Lienard Wiechert Potentials Power Radiated from a moving charge 2 2 2 2 2

3 Relativistic Decay 3 3 3 3 3

Relativistic Decay Center of Mass Frame. Conservation of Momentum: Conservation of Energy: Solve for p, E: 4 4 4 4

Relativistic Decay Solve for p, E: Boost into Lab Frame: 5 5 5 5

Pion & Kaon Decays 6 6 6 6

7 Retarded Time 7 7 7 7 7

Fields at the Speed of Light Einsteinian causality requires that no information propagate faster than the speed of light . The changes in E & B fields propagate at the speed of light, radiating outward from a changing source. See Java Demo. 8 8 8 8

Retarded Time A point in space is affected by the E-fields originating from a source in the past, at a time called the retarded time. In the past, the position of the source will have changed and that will in turn impact the time that should be evaluated. 9 9 9 9

Retarded Time & Light Cone 10 10 10 10

Retarded Potentials 11 11 11 11

12 Moving Point Charge 12 12 12 12 12

Moving Point Charge Solve by change of variables: 13 13 13 13

Change of Variables 14 14 14 14

Moving Point Charge Potentials We have derived: A similar derivation shows that: 15 15 15 15

Match what we found before? There is a trick we can use: 16 16 16 16

Lienard-Wiechert Potentials Actually this form is valid even for point sources not moving in a straight line at constant velocity. 17 17 17 17

Fields from a Point Charge 18 18 18 18

19 Power Radiated 19 19 19 19 19

Power Radiated Radiation in reference frame in which Beta is small: Integrate over Poynting for radiation: Linear acceleration: Circular acceleration: 20 20 20 20