View|4D

The View 4D menu provides a view of lattice properties with coupled vertical and horizontal beam motion.

Update 4D betas Updates initial beta-functions in 4D initial parameters block.
Close 4D Closes beta-functions and dispersions for a ring and updates information in 4D initial parameters block..
Beta4D Plots 4D beta functions.
Dispersion 4D Plots the horizontal, vertical and dispersion functions.
Size4D Plots the large and small semi-axes of the beam size ellipsoid and its rotation.
Size projections Plots the projection of beam sizes to the horizontal, vertical planes.
Phases 4D Plots the betatron phases.
Functions 4D Prints 4D Twiss parameters into the text window.
Functions at Elem. Print the beta-functions and dispersions at the end of element into a text window.
Control Controls the behavior for calculations of the X-Y coupled beta-functions.

View|Update 4D-betas

Updates values in 4D block (see XY coupled lattice treatment and 4D Beta-functions block).

View 4D|Close 4D

Closes the lattice for X-Y coupled case (finds the periodic solution for beta-functions and dispersions). If program can close the lattice it rewrites initial Twiss parameters in 4D Beta-functions block of the main window.

View 4D|Betas 4D

Plots 4D beta functions with initial values taken from 4D Beta-functions block of the main window (see also Graphical Window and XY coupled lattice treatment).

View 4D|Dispersion 4D

Plots the horizontal and vertical dispersion functions with initial values from 4D Beta-functions block of the main window (see also Graphical Window).

View 4D|Sizes 4D

Plots the large and small semi-axes of the beam size ellipsoid (a, b) and the ellipsoid tilt angle q. Initial values of beta-functions and emittances are taken from 4D Beta-functions block of the main window (see also View 4D|Size projections).

View 4D| Sizes Projections

Plots the projections of beam ellipsoid into horizontal and vertical planes and the parameter $\alpha_{xy}$ describing the beam ellipse orientation in accordance with the following formula: $$ \alpha_{xy} = \frac{ \tilde{y}}{ y_{\hbox{max}} } = \frac{ \tilde{x}}{ x_{\hbox{max}} } $$ Here the beam projections, $x_{\hbox{max}}$ and $y_{\hbox{max}}$, and corresponding them auxiliary coordinates are chosen as shown in the figure below

For $\alpha_{xy} = 0$ the main ellipse axes coincide with the coordinate frame axes. For $\alpha_{xy} = \pm 1$ the ellipse is transformed into a straight line. The corresponding ellipse equation is

$$ \frac{x^2}{x^2_{\hbox{max}}} - 2 \tilde{\alpha} \frac{xy}{x_{\hbox{max}}y_{\hbox{max}}} + \frac{y^2}{y^2_{\hbox{max}}} = 1 - \tilde{\alpha}^2 $$ while the ellipse half-axes and tilt are determined by following equations: $$ a = \frac{\sqrt{2(1-\tilde{\alpha}^2)} x_{\hbox{max}}y_{\hbox{max}}}{x^2_{\hbox{max}} + y^2_{\hbox{max}} + \sqrt{ (x^2_{\hbox{max}} - y^2_{\hbox{max}}})^2 + 4 \tilde{\alpha}^2 x^2_{\hbox{max}} y^2_{\hbox{max}} } $$ $$ b = \frac{\sqrt{2(1-\tilde{\alpha}^2)} x_{\hbox{max}}y_{\hbox{max}}}{x^2_{\hbox{max}} + y^2_{\hbox{max}} + \sqrt{ (x^2_{\hbox{max}} - y^2_{\hbox{max}}})^2 + 4 \tilde{\alpha}^2 x^2_{\hbox{max}} y^2_{\hbox{max}} } $$ $$ \phi = \arctan{\left[ \frac{2\tilde{\alpha}^2x_{\hbox{max}}y_{\hbox{max}}}{x^2_{\hbox{max}} - y^2_{\hbox{max}}}\right]} $$ Initial values of beta-functions and emittances are taken from 4D Beta-functions block of the main window.

View 4D|Phases 4D

Plots the 4D betatron phases with initial values from 4D Beta-functions block of the main window (see also Graphical Window and XY coupled lattice treatment).

View 4D|Functions 4D

Prints 4D Twiss parameters into the text window. Filter allows one to leave the desired elements in the list (See Filtering). Negative or zero step causes an output at the ends of elements only. If you need you can print functions only for elements in the range from Start from Element to Stop at element. Zero for these parameters means the entire range of output.

View 4D|Functions at Elem.

Prints the 4D beta-functions and dispersions at given element into the 4D text window. The element number is determined in a popped-up dialog box. Zero or negative number denotes the lattice end.

View 4D|Control

Brings up a dialog box with a check box which controls updating of beta-functions for X-Y coupled motion. If the box is checked, then before every calculation the values in 4D block (see XY coupled lattice treatment and 4D Beta-functions block) is updated. Otherwise parameters Nu_1, Nu_2 and U are chosen so that of four possible choices for the parameters the parameter Nu_1 would be closest to its value in the main window. If necessary they can be updated (calculated) using (Update 4D betas menu).