The transverse spacecharge force in trigaussian distribution
Abstract
In tracking, the transverse spacecharge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from spacecharge kicks when the beam is triGaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its triGaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be recalculated.
 Authors:
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 879032
 Report Number(s):
 FERMILABTM2331AD
TRN: US0701385
 DOE Contract Number:
 AC0276CH03000
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 43 PARTICLE ACCELERATORS; ACCELERATORS; DISTRIBUTION; SHAPE; SPACE CHARGE; Accelerators
Citation Formats
Ng, K.Y., and /Fermilab. The transverse spacecharge force in trigaussian distribution. United States: N. p., 2005.
Web. doi:10.2172/879032.
Ng, K.Y., & /Fermilab. The transverse spacecharge force in trigaussian distribution. United States. doi:10.2172/879032.
Ng, K.Y., and /Fermilab. Thu .
"The transverse spacecharge force in trigaussian distribution". United States.
doi:10.2172/879032. https://www.osti.gov/servlets/purl/879032.
@article{osti_879032,
title = {The transverse spacecharge force in trigaussian distribution},
author = {Ng, K.Y. and /Fermilab},
abstractNote = {In tracking, the transverse spacecharge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from spacecharge kicks when the beam is triGaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its triGaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be recalculated.},
doi = {10.2172/879032},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2005},
month = {Thu Dec 01 00:00:00 EST 2005}
}

The incoherent spacecharge selfforce tune shift of a biGaussian coasting beam is revisited. The distribution density of the incoherent horizontal or vertical spacecharge tune shift is computed numerically using a statistical method. Analytic approach has also been made with approximation. The results show a broad peak centered about 0.633 with a rms spread 0.168 of the linear spacecharge tune shift.

Distribution of incoherent space  Charge tune shift of a biGaussian beam
The incoherent spacecharge selfforce tune shift of a biGaussian coasting beam is revisited. The distribution density of the incoherent horizontal or vertical spacecharge tune shift is computed numerically using a statistical method. Analytic approach has also been made with approximation. The results show a broad peak centered about 0.633 with a rms spread 0.168 of the linear spacecharge tune shift. 
SPACE CHARGE WAVES IN AN ELECTRON BEAM OF GAUSSIAN CROSS SECTION. THE INTEGRAL EQUATION OF TRAVELING WAVE TUBES WITH ELECTRON BEAMS OF ARBITRARY CROSS SECTION
>The space charge waves of the Gaussian beam were studied. Space charge wavelengths, and thereby the plasma frequency reduction coefficients, were calculated. The physical problem is stated in equations. The general theory of the second order linear differential equations was applied and approximate solutions were constructed. The Gaussian beam was compared with the homogeneous beam and a beam with density varying as 1/r. A rigorous formulation is presented for the integral equation of traveling wave tubes with electron beams of arbitrary cross section. It is shown that the integral equations have general applicability in electron beamstructure interaction studies. A bibliographymore »