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Pueden llegar a acelerar partículas con energías de $30-40 MeV$, pero no más allá. +Para aumentar el voltaje sin que se produzcan descargas en el medio se suele encerrar todo el arreglo en contenedores con gases inertes. Pueden llegar a acelerar partículas con energías de $30-40 MeV$, pero no más allá. \subsection*{Aceleradores lineales} @@ -814,7 +814,7 @@ Esto se puede hacer con dipolos, pero dista mucho de poder enfocar, para lograr Si en un acelerador lineal el problema es la extensión, ¿porqué no intentar con uno circular? Usando el principio de resonancia, se construye un acelerador a partir de dos secciones metálicas en forma de $D$ huecas conectadas a un alto voltaje oscilante. El sistema se sitúa en un campo magnético también de alta intensidad, perpendicular a las secciones huecas. -El funcionamiento se parece un poco al del linac, más un campo magnético que produce la curvatura en la trayectoria. La fuente de iones o partículas cargadas se pone en la sección en medio de las dos $D$'s, como estas secciones tienen un alto voltaje es atraída hacia una de ellas, pero en esa sección fuera también logró sentir el campo magnético, lo que provoca que la partícula entre curvándose a la cavidad. Dentro de la $D$ ya no siente el campo magnético, pero la patada inicial bastó para curvar su trayectoria y el campo eléctrico ahora cambiado de signo produce que se acelere en dirección de la otra sección $D$, una vez que está en camino y sale a la región intermedia vuelve a sentir l patada del campo magnético, vuleve a curvarse pero además va aumentando su velocidad. +El funcionamiento se parece un poco al del linac, más un campo magnético que produce la curvatura en la trayectoria. La fuente de iones o partículas cargadas se pone en la sección en medio de las dos $D$'s, como estas secciones tienen un alto voltaje es atraída hacia una de ellas, pero en esa sección fuera también logró sentir el campo magnético, lo que provoca que la partícula entre curvándose a la cavidad. Dentro de la $D$ ya no siente el campo magnético, pero la patada inicial bastó para curvar su trayectoria y el campo eléctrico ahora cambiado de signo produce que se acelere en dirección de la otra sección $D$, una vez que está en camino y sale a la región intermedia vuelve a sentir la patada del campo magnético, vuelve a curvarse pero además va aumentando su velocidad. \begin{figure}[ht!] \begin{center} diff --git a/pres5.pdf b/pres5.pdf index 43dd546e11c7e9b46d87409d6547d77158438fa4..ab5a317e6fc26e81de5cb4ddec77c75c27ab10e3 100644 GIT binary patch delta 531803 zcma&NbyOYCwlx}@Ai>?;-92bm{OLEOc(T&h@`yY_~u)r7fSKJ)2IkiZ?7 z%y&26)SmN9``TB#J94#lgtlcqOITR^^HAOb8y)Fg_<{FNPN)_n9U0eB;)yv{2wllX z+BsnyWWMwWa`zN*IwzVd)uj285kOeDRP9Zi?Y5sw) zm9jq_ahM=Z4|a3yp_9bm{KdOADs+VQeX7y>m?suLC;5cb|62OdhBnF$?XU)miAr~< zc(2o3MTltvfBToZ&t1&`UXiD~PgnYBL%nozBr`d(gb z*Ev7ki!>)>VMUq8S&y4~sG@;Ip}=A#`8w4Zod!)8{&?m7#g}4R(?l>ldbHGO(qZ5 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Imagen adaptada de Chetvorno con licencia CC0} \end{center} \end{figure} + \begin{itemize} + \item SLAC acelera electrones hasta $50 GeV$ + \item 3 km de longitud de este acelerador. + \end{itemize} \end{frame} \begin{frame}{Óptica del haz} @@ -858,6 +862,39 @@ \end{figure} \end{frame} +\begin{frame}{Sincrotrón y su necesidad} + \begin{itemize} + \item Un \emph{linac} de $1 TeV$ necesitaría $60 km$ (de aquí a Cuernavaca más o menos). + \item McMillan y Veksler en 1945. + \item Inyectan partículas con energía $E_i$, momento $\rho_i$ y se sustenta un radio de curvatura $\rho$. + \item Cavidades $rf$ con frecuencia $\omega$ + \item El radio del anillo $R$ es mayor a $\rho$. + \end{itemize} +\end{frame} + +\begin{frame}{Análisis} + \begin{itemize} + \item $rf$ aún no se enciende. + \begin{equation*} + T=\frac{2\pi R}{v} = \frac{2\pi R E_i}{p_ic^2} \text{, ya que } \beta = \frac{pc}{E} + \end{equation*} + \item La frecuencia circular + \begin{equation*} + \Omega = \frac{2\pi}{T} = \frac{p_ic^2}{RE_i} + \end{equation*} + \item El campo magnético necesario + \begin{equation*} + B=\frac{p_ic}{|q|\rho} + \end{equation*} + \end{itemize} +\end{frame} + +\begin{frame}{Prendemos el sincrotrón} + \begin{align*} + \omega =& k\Omega = \frac{kc}{R}\frac{pc}{E} \overset{E=pc}{\rightarrow} \frac{kc}{R} + \end{align*} +\end{frame} + \begin{frame}{Método Monte Carlo} \begin{itemize} \item Tratamiento estadístico en experimentos @@ -941,7 +978,7 @@ \end{equation*} Consideramos $1000$ núcleos de ${}^{208}Tl$ \begin{itemize} - \item $tau_{{}^{208}Tl}=3.053$ minutos + \item $\tau_{{}^{208}Tl}=3.053$ minutos \item Decae a ${}^{208}Pb$ \end{itemize} \end{frame}