THE MICROWAVE GYRATOR 9 



The equation of motion of the magnetization per unit volume can 

 thus be written: 



4^=yMXH (6) 



where: 



M = Magnetization of medium 



H = Macroscopic internal magnetic field 



The above equation, however, does not include damping. The damping 

 force, regardless of its origin, must be so introduced into the above 

 equation that it tends to cause the electron's axis of rotation to line up 

 with the field direction. It has been shown by Yager, Gait, Merritt 

 and Wood " that the shape of the resonance absorption line can be 

 accounted for if the damping term is introduced in the following way: 



^ = tM X i/ - ^ [M X (M X ^)] (7) 



The vector M X (M X H) is simply a vector which is in the proper 

 direction to act as a damping force (torque) and the coefficient is chosen 

 so as to give the correct units along with the parameter, a, which must 

 be determined experimentally and which gives the magnitude of the 

 damping torque. 



Equation 7 then is the equation of motion of the magnetization of 

 an arbitrarily shaped l^ody under the action of an arbitrary internal 

 field, H. In the appendix, it is shown that if a steady magnetic field, 

 Ha , is applied along the s axis and then a small alternating field is ap- 

 plied in an arbitrary direction to a sample which is infinite in size, the 

 equation relating the resulting alternating flux density, b, and the ap- 

 plied alternating field, h is : 



bx = M^x — jKhy 



by = jKhx + iihy (8) 



be = hs 

 where 



M = M'-iM" (9) 



K = K' - jK" (10) 



Equations which give n and K in terms of the applied magnetic field 

 and fundamental atomic constants are given in the appendix. 



