Beam energy measurement

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Beam energy measurement

After loading the data from the superharps at the entrance (IHA3C07A and IHA3C07B) and at the exit (IHA3C17A and IHA3C17B) of the hall C arc beamline, the $\fbox{Calculate dP/P0}$ option will be enabled? This menu option allows users to calculate the beam incident energy through some conditions:

If the full width of the first peak of harp IHA3C07A is less than twice the full width of the first peak of harp IHA3C17A, then the beam is not dispersive enough to perform the calculation, and an error will be generated.
Prior to the calculation, one has to verify the dispersion and the amplification factor at the exit of the arc related to the hall C beamline optic settings. The default values are now 12.5 cm and 3, respectively.
Only the MCC operators are allowed to perform the beam energy calculation since there is a setup procedure to follow [] (see appendix ). The users can re-evaluate this calculation by asking for the setting current of the arc dipole magnets and loading all the corresponding superharp data.

The basic idea behind the calculation is as follows. Suppose a particle with mass and charge is subjected to a magnetic field $\vec{B}$ perpendicular to the plane of the particle's motion, causing it to travel in a circular path of radius . The beam momentum is determined via:

$\begin{displaymath} P_0 = \frac{e}{\Theta}\int Bdl \end{displaymath}$

(2.11)

where $\int Bdl$ is the magnetic field integral over the path of the electron beam and $\Theta = 34.3^\circ$ is the bending angle through which the electron beam is deflected. $\int Bdl$ is determined by mapping bending magnets absolutely with a combination of NMR and Hall probes. Taking

as a constant, this leads to the uncertainty relation:

$\begin{displaymath} \frac{\Delta P}{P_0} = \sqrt{\Big (\frac{\Delta \int Bdl}{\i... ...ig )^{2} + \Big (\frac{\Delta \Theta}{\Theta}\Big )^{2}} \; . \end{displaymath}$

(2.12)

The inclusion of the beam incident angle is taken into account by utilizing the Lorentz force:

$\begin{displaymath} \vec{F}=-e\vec{v}\times \vec{B} = m_e\vec{a}, \end{displaymath}$

(2.13)

where $\vec{a}$ is the acceleration and

the mass of the electron. Projecting on the three cartesian axis (z-beam direction, x-transverse horizontal and y-transverse vertical):

$\begin{displaymath} \left \{ \begin{array}{lll} a_x & = & -\frac{evB}{m_e} \\ a... ...heta _y) \\ v_z & = & vcos(\theta _x) \\ \end{array}\right . \end{displaymath}$

(2.14)

$\begin{displaymath} \Leftrightarrow \left \{ \begin{array}{lll} x & = & -\frac{e... ...y_0 \\ z & = & vcos(\theta _x)t + z_0 \\ \end{array}\right . \end{displaymath}$

(2.15)

We are in a case where:

. Therefore:

$\begin{displaymath} \left \{ \begin{array}{lll} t & = & \frac{z}{vcos(\theta_x)}... ...cos(\theta _y)}{cos(\theta _x)}z + y_0 \\ \end{array}\right . \end{displaymath}$

(2.16)

The system in (2.15) characterizes the trajectories of the particle along

and

as a function of its position inside the magnetic region along

The expression of represents the trajectory of the particles in the dispersion plane (where the particles are subject to the magnetic field):

$\begin{displaymath} x = -\frac{eB}{2Pcos^2(\theta _x)}z^2 + tan(\theta _x)z + x_0, \end{displaymath}$

(2.17)

where $x = x_{17}$ , $x_0 = x_{07}$ and $\theta _x = \theta _{07}$ are determined by using the superharps at the entrance (IHA3C07) and at the exit (IHA3C17) of the arc. The beam momentum

corrected from incident beam angle can then be evaluated.

Next: Further Help Up: Superharp Systems Previous: Using the Program

Hall-C Staff
2002-11-04