Protons are injected into a linear accelerator so that they have K=250 keV as they coast through

step 1 So in this case, the same case, our number of gaps is n is equal to nine. So after the nine gap,

Protons are injected into a linear accelerator so that they...

Protons are injected into a linear accelerator so that they have $K=250 \mathrm{keV}$ as they coast through the first drift tube. The frequency of the AC voltage applied to the tubes is $50 \mathrm{MHz}$ and the peak potential difference across each gap is $200 \mathrm{kV}$. Consider a proton that passes from the first to the second tube properly synchronized at the peak potential drop. (a) How long must the second tube be if the proton is to arrive at the next gap in proper synchronization with the accelerating voltage? (b) How long must the tenth tube be?

Key Concepts

Kinetic Energy and Particle Velocity

The kinetic energy of a charged particle determines its velocity. As particles are accelerated and their kinetic energy increases, their velocity also increases. This relationship is crucial when designing the drift tube lengths, as the time-of-flight through each tube must be adjusted according to the particle's changing speed.

Transit Time

Transit time is the time it takes for a particle to travel through a section of the accelerator, such as a drift tube. In a drift tube linac, this time must be matched with a specific portion of the electrical cycle so that the particle arrives at the next accelerating gap in the proper phase of the oscillating field.

Alternating Current (AC) Acceleration

AC acceleration utilizes an alternating electric field with a specific frequency to impart energy to charged particles. The timing, phase, and frequency of this field are critical, as the design of accelerator components, such as drift tubes, is based on ensuring that the particles benefit from the peak of the accelerating voltage at the correct moments.

Drift Tube Linac (DTL)

Drift tube linear accelerators are a specific type of accelerator where particles traverse a series of hollow conducting tubes separated by gaps with accelerating electric fields. The tubes are designed to shield the particles from the decelerating phase of the alternating field while allowing them to gain energy during each gap, making tube length critical for maintaining synchronization.

Linear Accelerator (Linac)

A linear accelerator is a device that uses electric fields to accelerate charged particles in a straight line. It is widely used in applications ranging from medical treatments to fundamental physics research, where particles are sped up to high energies in a controlled environment.

Synchronization in Particle Acceleration

Synchronization refers to the process of coordinating the arrival time of the charged particles with the phase of the alternating electric field in the accelerator. This ensures that particles consistently experience the field when it is in the correct polarity to accelerate them, which is essential for effective energy gain and overall accelerator performance.

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