Sec. 9.3] 



MASS SPECTROGRAPHS 



281 



however, that energetically inhomogeneous ion beams cannot be properly 

 focused. The ion source, therefore, must provide ions of as nearly homo- 

 geneous energy as possible when the greatest accuracy and resolution is 

 required. 



The focus at the 180-deg position where the collecting electrode is placed 

 is not a line image but has a natural width 5 given by 8 = Ra 2 , where a is 

 one-half the angular beam divergence in radians at the source. This places 

 a limit on the separation of two values of m/e with nearly equal magnitude, 

 or alternatively, determines the maxi- 

 mum allowable angle of beam diver- 

 gence for a required resolution, since 

 the separation of the two foci must _ 

 be greater than the image width, or 

 approximately 



a 2 < 2 





Assuming the maximum geometri- 

 cal resolving power to be defined as 

 the smallest difference in mass Am 

 for which the images are just separated, it is then given by the expression 



Fig. 61. Dempster mass spectrograph. 



m o 2 



Am 



This assumes the ion beam to be perfectly homogeneous in velocity; if 

 it is not, a term involving AV must be added. 



9.3. 60-Degree (Nier-Type) Mass Spectrometer. A mass spectrometer 

 employing a uniform 60-deg magnetic field has been developed into a highly 

 practical instrument by Nier for routine gas analyses and isotope-abundance 

 measurements [9,23]. Aside from its source and electrical components, the 

 chief advantage of this type of instrument is in the relatively small magnet 

 required to maintain the wedge-shaped field. On the other hand, since an 

 electrostatic analyzing field is not used, this type of geometry does not, 

 strictly speaking, provide either velocity or directional focusing and its 

 resolution therefore depends on the efficiency of the ion source and the degree 

 of collimation of the ion beam. 



The geometrical arrangement of the source, magnetic field, and ion col- 

 lector is shown in Fig. 62. Some adjustment must be provided for moving 

 the magnet along the axis A- A since the fringing field of the magnet alters 

 somewhat the exact geometry. In the uniform portion of the field, the ion 

 trajectory radius is given by 



