高密度荷電粒子ビームの自己組織化と安定性

Size: px

Start display at page:

Download "高密度荷電粒子ビームの自己組織化と安定性"

ゆずさねぎたや
5 years ago
Views:

1 Hiromi Okamoto Graduate School of Advanced Sciences ofmatter, Hiroshima University ( ( ) $)$ ( ) ( ) [1],, $*1$ 2 ( $m,$ q) $*1$ ;

$$\kappa_{x}$ $\kappa_{y}$ 2 $H_{t}=c\sqrt{(p-qA)^{2}+m^{2}c^{2}}+q\Phi$ (2.1) $c$ $\Phi$ $A$ $t$ $s$ $\Phi$ $A$ $*2$ (2.$

2 $\kappa_{x}$ $\kappa_{y}$ 2 $H_{t}=c\sqrt{(p-qA)^{2}+m^{2}c^{2}}+q\Phi$ (2.1) $c$ $\Phi$ $A$ $t$ $s$ $\Phi$ $A$ $*2$ (2.1) $s$ ( - $)$ ( ) $s$ [2]: $H_{s}= \frac{1}{2}(p_{x}^{2}+p_{y}^{2})+\frac{1}{2}[k_{x}(s)x^{2}+k_{y}(s)y^{2}]+i\phi_{sc}$ (2.2) $(x,y)$ $(p_{x}, p_{y})$ $I$ $\iota$ ) 3 ( ) $K_{X}(s)$ Ky(s) $\}$ $s$ (2.2) (smooth approximation) $\overline{h}_{s}=\frac{1}{2}(p_{x}^{2}+p_{y}^{2})+\frac{1}{2}(\kappa_{x}^{2}x^{2}+\kappa_{y}^{2}y^{2})+i\phi_{sc}$ (2.3) ( ) (2.2) $*2$ 1

3 $\kappa_{z}^{2}$ $\epsilon_{0}$ 3 $H=H_{s}+ \frac{1}{2}[p_{z}^{2}+k_{z}(s)z^{2}]$ (2.4) 3 $K_{z}(s)$ $\kappa_{z}$ $\kappa_{x(y)}$ (2.4) ( ) (2.1) (2.4) $x$ $p_{z}$ (2.2) (2.4) $\nabla^{2}\phi_{sc}=-n\underline{q}$ (2.5) $\epsilon_{0}$ $n$ $n\ovalbox{\tt\small REJECT}$ $f$ : $n(x,y;s)= \iint f(x,y,p_{\chi},p_{y};s)dp_{x}dp_{y}$ (2.6) f $fi$ $\frac{\partial f}{\partial s}+[f, H_{s}]=0$ (2.7) $[,$ (2.7) $]$ $H_{s}$ $H_{s}$ (2.5) (2.5) (2.6) $f$ (2.7) (2.5) (Vlasov) PIC (Particle In Cell)

4 4 $n$ $n$ 3 ( ) (2.2) (2.4) ( ) 1960 Sacherer[3] Gluckstem[4] [5], [6] $L$ $K_{x(v)}(s)=K_{x(y)}(s+L)$ $f_{0}$ $s$ $L$

$3) ; $s$ $\overline{h}_{s}$ $d\overline{h}_{s}/ds=0$ $f_{0}(\overline{h}_{s})$ $f_{0}$ $f_{0}\propto\exp(-\overline{h}_{s}/t)$ $(T$ $)$ $ _{}f_{0}$ $\overline{h}_{s}$$

5 5 (matched beam) (2.7) $/ds=0$ (2.3) (2.3) ; $s$ $\overline{h}_{s}$ $d\overline{h}_{s}/ds=0$ $f_{0}(\overline{h}_{s})$ $f_{0}$ $f_{0}\propto\exp(-\overline{h}_{s}/t)$ $(T$ $)$ $ _{}f_{0}$ $\overline{h}_{s}$ $df_{0}(\overline{h}_{s})/d\overline{h}_{s}\leq 0$ [7,8]. $*3$ (2.2) Kapchinshy-Vladimirsky ( $KV$) [9] ( ) : $\phi_{sc}=\frac{1}{2}[q_{x}(s)x^{2}+q_{y}(s)y^{2}]$ (3.1) $Q_{x(y)}(s)$ $K_{x(y)}(s)$ $\tilde{k}_{x(y)}(s)\equiv K_{x(y)}(s)+IQ_{x(y)}(s)$ (2.2) $H_{s}= \frac{1}{2}[p_{x}^{2}+\tilde{k}_{x}(s)x^{2}]+\frac{1}{2}[p_{y}^{2}+\tilde{k}_{y}(s)y^{2}]$ (3.2) $x$ $y$ (2.2) (3.2) (action) $x$ $*3$

$$\epsilon_{x}$ $\epsilon_{y}$ 6 $J_{X}=\beta_{X}(s)p_{X}^{2}+2\alpha_{X}(s)xp_{X}+\gamma_{X}(s)x^{2}$ (3.$

6 $\epsilon_{x}$ $\epsilon_{y}$ 6 $J_{X}=\beta_{X}(s)p_{X}^{2}+2\alpha_{X}(s)xp_{X}+\gamma_{X}(s)x^{2}$ (3.3) $J_{X}$ [10]; $M_{x} \int ds=0$ $\beta_{x}(s)$ $\frac{d^{2}\sqrt{\beta_{x}}}{ds^{2}}+k_{x}(s)\sqrt{\beta_{x}}-\frac{1}{(\sqrt{\sqrt{}x})^{3}}=0$ (3.4) $\alpha_{x}=-(d\beta_{x}/ds)/2$ $\gamma_{x}=(1+\alpha_{x}^{2})/\beta_{x}$ $y$ $x$ (3.3) $J_{X}$ ( ) $J_{x}$ $y$ $J_{y}$ $x$ (2.5) (3.1) $f_{0}$ Kapchinsky Vladimirsky $f_{0}(j_{x},j_{y}) \propto\delta(\frac{j_{x}}{\epsilon_{x}}+\frac{j_{y}}{\epsilon_{y}}-1)$ (3.5) (3.1) $x$ $y$ $\delta(z)\ovalbox{\tt\small REJECT}$ Dirac (2.6) $KV$ ( ) $KV$ $KV$ $KV$ $-A$ : PIC

7 7 ( ) ( $)$ $H_{P}= \frac{1}{2}(p_{\chi}^{2}+p_{\mathcal{y}}^{2})+\frac{1}{2}k_{rf}(t)(x^{2}-y^{2})+i_{p}\phi_{sc}$ (4.1) $I_{P}$ $K_{RF}(t)$ [11] (2.5) $f$ (2.7) (2.2) (4.1) $*4$ [12]. $*4$ (2.2) (4.1)

$8 4.2 [13] $I_{G}$ $H_{G}=$

8 8 4.2 [13] $I_{G}$ $H_{G}= \frac{1}{2}(p_{x}^{2}+p_{y}^{2}+p_{z}^{2})+i_{g}\phi_{g}$ (4.2) [13], $*5$ $-J\triangleright$ ( ) $*5$ ( )

9 9 (4.2). 5 : $\frac{\partial f}{\partial s}+p\cdot\frac{\partial f}{\partial r}-\nabla(u_{ext}+\phi)\cdot\frac{\partial f}{\partial p}=0$ (5.1) $\phi$ $\nabla^{2}\phi=-\mu\int fd^{3}r$ (5.2) (5.1) $U_{ext}(r,s)$ $ $ $U_{ext}= \frac{1}{2}[k_{x}(s)x^{2}+k_{y}(s)y^{2}+k_{z}(s)z^{2}]+\delta U(r,s)$ (5.3) $*6$ $\delta U(r,s)\ovalbox{\tt\small REJECT}$ $U_{ext}$ $\overline{u}_{ext}=\frac{1}{2}(\kappa_{x}^{2}x^{2}+\kappa_{y}^{2}y^{2}+\kappa_{z}^{2}z^{2})$ (5.4) $U_{-}.$ $=0$ (5.2) $\mu$ ( ) (5.1) (5.2) (5.4) $\delta U$ (5.3) ( ) $KV$ (3.5) $KV$ $*6$

$10 $KV$ ( $\delta U\neq 0$ ) (structure resonance), (non-structure$

10 10 $KV$ ( $\delta U\neq 0$ ) (structure resonance), (non-structure resonance) $KV$ ( $KV$ 50 ) ( ) ( ), (5.4) ( ), ( ) $-\Lambda$ ( )

11 11 [1] A.W. Chao and M. Tigner (Ed.), Handbook of Accelerator Physics and Engineering, World Scientific, Singapore, 1999, ISBN [2] M. Reiser, Theory and Design of Charged Particle Beams, John Wiley & Sons, INC., 1994, ISBN , and references therein. [3] F.J. Sacherer, Ph.D. Thesis, UCRL 18454, [4] R.L. Gluckstem, Proceedings of the Linac Conference, Fermilab, Batavia, IL, 1970, $p.$ 811. [5] I. Hofinann, L. J. Laslett, L. Smith and H. Haber, Part. Accel. 13 (1983) 145. [6] H. Okamoto and K. Yokoya, Nucl. Instrum. Meth. 482 $A$ (2002) 51. [7] W. Newcomb, as reported by I. B. Bemstein, Phys. Rev. 109 (1958) 10. [8] C.S. Gardner, Physics Fluids 6 (1963) 839. [9] I.M. Kapchinsky and V.V. Vladimirsky, Proceedings of the Intemational Conference on High Energy Accelerators, CERN, Geneva, 1959, p [10] E.D. Courant and H.S. Snyder, Ann. Phys. 3 (1958) 1. [11] P.K. Ghosh, Ion Traps, Oxford Science, Oxford 1995, ISBN [12] H. Okamoto and H. Tanaka, Nucl. Instrum. Meth. 437 $A$ (1999) 178. [13] J. Binney and S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics, Princeton University Press, 1987, ISBN

加速器の基本概念 V : 高周波加速の基礎

加速器の基本概念 V : 高周波加速の基礎 .... V : KEK koji.takata@kek.jp http://research.kek.jp/people/takata/home.html 2015 2015 4 16 1 2 (1) 3 (2) 4 5 6 ERL: Energy Recovery Linac LCLS: Linac Coherent Light Source LC : µ-µ Koji Takata (KEK)