Truncated thermal equilibrium distribution for intense beam propagation
An intense charged particle beam with directed kinetic energy (γ_{b}-1)m_{b}c^{2} propagates in the z direction through an applied focusing field with transverse focusing force modeled by F_{foc}=-γ_{b}m_{b}ω_{β⊥}^{2}x_{⊥} in the smooth-focusing approximation. This paper examines properties of the a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2003-02-01
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| Series: | Physical Review Special Topics. Accelerators and Beams |
| Online Access: | http://doi.org/10.1103/PhysRevSTAB.6.024402 |
| _version_ | 1818525512087109632 |
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| author | Ronald C. Davidson Hong Qin Steven M. Lund |
| author_facet | Ronald C. Davidson Hong Qin Steven M. Lund |
| author_sort | Ronald C. Davidson |
| collection | DOAJ |
| description | An intense charged particle beam with directed kinetic energy (γ_{b}-1)m_{b}c^{2} propagates in the z direction through an applied focusing field with transverse focusing force modeled by F_{foc}=-γ_{b}m_{b}ω_{β⊥}^{2}x_{⊥} in the smooth-focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F_{b}(r,p_{⊥})=Aexp(-H_{⊥}/T[over ^]_{⊥b})⊕(H_{⊥}-E_{b}), where A, T[over ^]_{⊥b}, and E_{b} are positive constants, and H_{⊥} is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n_{b}(r)=∫d^{2}pF_{b}(r,p_{⊥}), and transverse temperature, T_{⊥b}(r)=[n_{b}(r)]^{-1}∫d^{2}p(p_{⊥}^{2}/2γ_{b}m_{b})F_{b}(r,p_{⊥}), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius r_{b} with n_{b}(r≥r_{b})=0, where r_{b} depends on the value of E_{b}/T[over ^]_{⊥b}. In addition, unlike the choice of a semi-Gaussian distribution, F_{b}^{SG}=Aexp(-p_{⊥}^{2}/2γ_{b}m_{b}T[over ^]_{⊥b})⊕(r-r_{b}), the truncated thermal equilibrium distribution F_{b}(r,p) depends on (r,p) only through the single-particle constant of the motion H_{⊥} and is therefore a true steady-state solution (∂/∂t=0) of the nonlinear Vlasov-Maxwell equations. |
| first_indexed | 2024-12-11T06:10:05Z |
| format | Article |
| id | doaj.art-e57fd2e762694292855ddb36131ea080 |
| institution | Directory Open Access Journal |
| issn | 1098-4402 |
| language | English |
| last_indexed | 2024-12-11T06:10:05Z |
| publishDate | 2003-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Special Topics. Accelerators and Beams |
| spelling | doaj.art-e57fd2e762694292855ddb36131ea0802022-12-22T01:18:09ZengAmerican Physical SocietyPhysical Review Special Topics. Accelerators and Beams1098-44022003-02-016202440210.1103/PhysRevSTAB.6.024402Truncated thermal equilibrium distribution for intense beam propagationRonald C. DavidsonHong QinSteven M. LundAn intense charged particle beam with directed kinetic energy (γ_{b}-1)m_{b}c^{2} propagates in the z direction through an applied focusing field with transverse focusing force modeled by F_{foc}=-γ_{b}m_{b}ω_{β⊥}^{2}x_{⊥} in the smooth-focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F_{b}(r,p_{⊥})=Aexp(-H_{⊥}/T[over ^]_{⊥b})⊕(H_{⊥}-E_{b}), where A, T[over ^]_{⊥b}, and E_{b} are positive constants, and H_{⊥} is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n_{b}(r)=∫d^{2}pF_{b}(r,p_{⊥}), and transverse temperature, T_{⊥b}(r)=[n_{b}(r)]^{-1}∫d^{2}p(p_{⊥}^{2}/2γ_{b}m_{b})F_{b}(r,p_{⊥}), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius r_{b} with n_{b}(r≥r_{b})=0, where r_{b} depends on the value of E_{b}/T[over ^]_{⊥b}. In addition, unlike the choice of a semi-Gaussian distribution, F_{b}^{SG}=Aexp(-p_{⊥}^{2}/2γ_{b}m_{b}T[over ^]_{⊥b})⊕(r-r_{b}), the truncated thermal equilibrium distribution F_{b}(r,p) depends on (r,p) only through the single-particle constant of the motion H_{⊥} and is therefore a true steady-state solution (∂/∂t=0) of the nonlinear Vlasov-Maxwell equations.http://doi.org/10.1103/PhysRevSTAB.6.024402 |
| spellingShingle | Ronald C. Davidson Hong Qin Steven M. Lund Truncated thermal equilibrium distribution for intense beam propagation Physical Review Special Topics. Accelerators and Beams |
| title | Truncated thermal equilibrium distribution for intense beam propagation |
| title_full | Truncated thermal equilibrium distribution for intense beam propagation |
| title_fullStr | Truncated thermal equilibrium distribution for intense beam propagation |
| title_full_unstemmed | Truncated thermal equilibrium distribution for intense beam propagation |
| title_short | Truncated thermal equilibrium distribution for intense beam propagation |
| title_sort | truncated thermal equilibrium distribution for intense beam propagation |
| url | http://doi.org/10.1103/PhysRevSTAB.6.024402 |
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