MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 451 



For low enough powers x" is not a function of Hi (and even for very high 

 powers never drops off faster than \/Hi), so that for a large power ab- 

 sorption one would like a large RF magnetic field. This suggests a re- 

 sonant cavity which indeed is used in all experimental setups. The Q of 

 a cavity into which a paramagnetic sample is placed is given by 



'dV. 



1 f H' 



Q ^ Energy Stored ^ Sr Jy^ ^ ,^. 



Average Power Dissipated IT 2 // 



Pi -f - CO / Hix dV, 

 z Jv, 



where Pi = power dissipated in the cavity in the absence of any para- 

 magnetic losses, Vs is the sample volume and Yc the cavity volume. 



Assuming that the paramagnetic losses are small in comparison with 

 Pi we get 



f H;YdVs \ 



Hi' dVc / (4) 



/. 



AQ = QoAiirx V 



where Qo is the cavity Q in the absence of paramagnetic losses and 17 

 is the filling factor and depends on the field distribution in the cavity 

 and the sample. For example, in a rectangular cavity excited in the TEioi 

 mode 



T7 A 



(5) 



where d is the length of the cavity and a the width along which the E 

 field varies. In the above example it was assumed that the sample is 

 small in comparison to a wavelength and is placed in the max. Hi field. 



IV. COUPLING TO RESONANT CAVITIES FOR MAXIMUM OUTPUT 



Having established the Q changes associated with the resonance 

 absorption, we will next determine the proper coupling to the resonant 

 cavity in order that the Q changes result in a maximum change in trans- 

 mitted or reflected power (or \-oltage). The derivation will be based on 

 the assumption that we have a fixed amount of power available from 

 our source and that the Q change is not a function of the RF power (no 

 saturation effects). 



