Cyclotron

Also called

dees · particle accelerator · proton circles in a magnetic field · cyclotron frequency · magnetic force on a moving charge · Lorentz force · radius grows with speed · alternating voltage · exit window · deflector · velocity selector · mass spectrometer · crossed fields · Lawrence · qvB · साइक्लोट्रॉन · आवेशित कण · चुंबकीय क्षेत्र · कण त्वरक

Topics

• A cyclotron accelerates charged particles such as protons to high energies using an electric and a magnetic field.
• A uniform magnetic field makes a charge move in a circle: qvB = mv²/r, so the radius r = mv/qB grows with speed.
• The time for one revolution, T = 2πm/qB, does not depend on the speed or the radius (as long as v ≪ c).
• An alternating voltage across the gap between the two dees reverses every half turn, at the frequency qB/2πm.
• Inside a dee the electric field is zero; the particle is pushed only while crossing the gap, gaining qV each time.
• With each push the speed and radius grow, so the path is a spiral that ends at the deflector and exit window.
• The final kinetic energy q²B²R²/2m is fixed by the dee radius R and the field B.
• Crossed E and B fields let through only particles with v = E/B; a magnetic field then sorts them by mass, r = mv/qB.

About this model

A GLB file of about 414 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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