The effect of two quadrupoles, alternately focusing and defocusing

A diverging beam comes from the left. As it passes through the focusing quadrupole , it gets focused: its divergence gets smaller as the strength of the quadrupole is increased.

The beam then passes through the defocusing quadrupole which defocuses it. Under certain conditions, the net effect is focusing.
You can play with the focusing and defocusing strengths with the scrollbars and see the effect for yourself.
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At this point you may be asking yourself "If the aim of the game is to try and focus the beam, why on earth do you need defocusing quadrupoles in the first place ???"
The reason is that we cannot do otherwise: because of the nature of the magnetic field, if a magnetic quadrupole focuses the beam horizontally, it will defocus it vertically. This is the topic of the next lesson: How does an actual quadrupole work?