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The limiting value of the current density in a beam compressed by an arbitrarily large magnetic field has been derived from Liouville's theorem and the adiabatic invariance theorem. For sufficiently large compression ratios the limiting values are (1+eV/kt), as a result expected from the Langmuir‐Pierce expression. Some of the effects due to the use of a finite magnetic field have been examined with particular reference to the current density obtainable at the planes where cathode images are formed. The transit time scatter imposes an upper limit on the maximum compression ratio for which these cathode images can be utilized.