Round Beam-Beam Map with Tune Modulation

Choose a value for the base tune Q0 and for the depth of the tune modulation parameter q. Then choose the "tune shift parameter" xi (the strength of the single round beam-beam kick) and the period of the tune modulation Tm (in turns). Finally, enter the number of iterations. Hit return to make the number appear on the button that intially says "0 more". For example, you might want to try Q = 0.331, q = 0.001, xi = 0.006, Tm = 194, and 500 iterations.

Then click the mouse in the window where you would like to launch a test particle. You may repeat this step several times. It is easy to get massive chaos with a little tune modulation turned on!

The following equations are used to generate the motion: 

 
	t  =  0
	until done {
		t  =  t + 1
		Q  =  Q0 + q sin(2 pi t / Tm)

		Rotate (x,x') by 2*pi*Q
		x'  =  x' - 4 pi xi (2/x) [1 - exp(-x*x/2)]

		if  t  is divisible by  Tm,  plot (x,x') in polar coordinates
	}

Notes
=====
1) The vertical axis is BETATRON AMPLITUDE, a = sqrt(x*x + x'*x'), running from a = 0 to a = 6.
2) The horizontal axis is BETATRON PHASE, phi, where tan(phi) = x/x', running from phi = 0 to phi = 2 pi.
3) Be patient! Wait for "DONE" to appear in the bottom right corner before launching another particle.

Take a look at some other maps: Last modified: Wed Nov 19 11:59:41 EST