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A focusing scheme employing two counteracting periodic fields without the use of any magnet is shown to be superior to schemes which involve only one periodic focusing field. The potential valley formed by the combination of these two counteracting fields is steeper than all previous focusing systems and thus is capable of maintaining a very stable beam flow. The combined field also gives rise to proper cancellation of the space charge field. This field cancellation not only results in an ideal focusing for high-density beam but also, compensates for the potential depression inside the beam. With a periodic voltage variation of 5 per cent on the beam, it is theoretically possible to focus with an ideal gun, an electron beam of perveance in the order of 10-5 amp/volt3/2. With a nonoptimized gun, a beam of perveance 2Ã10-6 amp/volt3/2 has been focused to a 97 per cent current transmission. A 10-db rf gain was observed at a frequency of 2950 mc.