Henon map with damping and excitation

Choose a value for the tune Q, and for the strength of the single sextupole b2. Then, enter the number of iterations. Hit return to make the number appear on the button that intially says "0". This is the basic Henon map.

If you wish, you may also simulate the effects of adding synchrotron damping and excitation, by inserting non-zero values for the "damping decrement" Delta and for the "quantum excitation step size" Alpha. The damping decrement is the inverse of the damping time, and has typical values in the range from 0.0001 to 0.01. The excitation step size is the standard deviation of the Gaussian distributed random walk, applied once per turn (see equations, below).

Then click the mouse in the window where you would like to launch a test particle. You may repeat this step several times. When the damping is turned on at a small enough level (without excitation), any resonance islands that were present turn into "attractors" - particles enter, but they do not leave!. The following equations are used to generate the motion: 

 
	until done {
		Rotate (x,x') by 2*pi*Q
		x'  =  x' - b2*x2

		x  =  x  * (1 - Delta) + Alpha * G
		x' =  x' * (1 - Delta) + Alpha * G
	}
where G is a random number with a Gaussian distribution, and average = 0, standard deviation = 1

Also note that the "window" size is from -1 to +1 in both x and x'.

For example, you might want to try Q = .252, b2 = 1.0, with 1000 iterations and synchrotron radiation turned off. You might also want to try Delta = 0.01, and Alpha = 0.1

Take a look at some other maps: Last modified: Fri Nov 14 09:11:38 EST