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electron device in the ratio R, if we keep all voltages the same, and if we 

 change all magnetic fields in the ratio 1/i?, electron current will remain the 

 same (provided the cathode is still capable of giving space charge limited 

 emission). Electron paths will remain exactly similar, though smaller; 

 the power into the electron beam will remain the same, but what will happen 

 to the power dissipation capabilities of the device and what will happen to 

 the temperature? 



In a device cooled by radiation alone and with cool surroundings, the 

 radiating area varies as Rr, and since the radiation per unit area varies as 

 T^, the temperature will vary as JKT . 



In considering a case of cooling by conduction alone, think of a rod 

 carrying a certain amount of power away. If all the dimensions of a rod 

 are changed by a factor R, the length will be changed by a factor R, the cross 

 sectional area will change by a factor R^, and if the thermal conductivity 



CURRENT, 

 VOLTAGE, POWER 



TEMPERATURE, 

 RADIATION ' 

 COOLING 



LINEAR DIMENSION 



TEMPERATURE, 

 CONDUCTION 

 COOLING 

 MAGNETIC FIELD 

 Fig. 12 — Variation of magnetic field and temperature in scaling an electronic device. 



remains constant the temperature will vary as R~^. This is a faster rate of 

 variation than in the case of cooling by radiation, and hence as the system 

 is scaled to a smaller and smaller size, cooling by conduction will become 

 negligible and radiation cooling only will remain eflfective and will determine 

 the temperature. 



Figure 12 gives an idea of the variation of various quantities discussed. 



We want to make electronic devices smaller for a number of reasons; 

 perhaps chiefly to reduce transit time and so to secure operation at higher 

 frequencies. In doing this, we encounter the fundamental limitation of 

 reduced power dissipation capabilities and increased temperature. What 

 is the trouble? We have scaled everything. Or have we? The answer 

 is, we have not. The electrons, atoms, and quanta are still the same size. 

 Had we been able to scale these, we should have increased the heat con- 

 ductivity and the radiating power of our device, and all would have been 



