BUNCHING PHENOMENA DURING ELECTRON INJECTION INTO THE BETATRON. II. THEORY OF STARTING CONDITIONS

Journal Article · Mon Jan 01 04:00:00 EST 1962 · Czechoslov. J. Phys.

DOI:https://doi.org/10.1007/BF01689431· OSTI ID:4780523

Seidl, M

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments. The bunching is treated as a small perturbation of the stationary beam. The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance. Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in agreement with experiments. Such agreement may be considered as verification of the statement that the amplification of the disturbances is caused by the negative mass instability'' mechanism. ( auth)

• Research Organization: Inst. of Vacuum Electronics, Czechoslovak Academy of Sciences, Prague
• Sponsoring Organization: USDOE
• NSA Number: NSA-16-031134
• OSTI ID: 4780523
• Journal Information: Czechoslov. J. Phys., Journal Name: Czechoslov. J. Phys. Vol. Vol: 12
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BETATRONS
BUNCHING
DENSITY
DISTRIBUTION
ELECTRON BEAMS
ENERGY
EQUATIONS
ERRORS
INJECTION
MASS
MEASURED VALUES
MODULATION
NUMERICALS
PERTURBATION THEORY
PHYSICS
STABILITY
VELOCITY