What Causes Frequency Discrepancies in Particle Accelerator Calculations?

In the first problem, the frequency of the applied electric field in a 70 MeV betatron is calculated using the angular velocity of the electron. However, there seems to be a discrepancy between the calculated frequency and the answer given in the book. In the second problem, the total length of a linear accelerator is sought, but it is a time consuming process and the person is looking for a better method. The conversation also briefly touches on the consideration of relativistic speed in the calculations.
  • #1
Amith2006
427
2
I need help. It’s urgent!
# Assume that in the 70 million electron volt (MeV) betatron, the radius of the stable electron orbit is 28 cm. Calculate the frequency of the applied electric field.
I have found the angular velocity of the electron (w) = 1.07 x 10^9
I assumed that the frequency of the electron= frequency of applied electric field
From that I found the frequency(f) of the
w = 2(pi)f
f = 1.7 x 10^8 Hz
But the answer given in my book is 1.7 x 10^6 Hz. Is it a typographic error?

# A linear accelerator for the acceleration of protons to 45.3 MeV is designed so that between any pair of accelerating gaps, the protons spend one complete radio frequency cycle inside a drift tube. The frequency of the radio frequency oscillator is 200 MHz. If the frequency of the accelerating potential is 1.49 x 10^6 volts, what is the total length of the linear accelerator?
I have found the length of the drift tubes individually. By adding the length of all the drift tubes, the length of the linear accelerator can be found out. But that is a time taking process. Is there is better way to find the length of the linear accelerator? I asked my lecturer, he also doesn’t know. Please reply fast because I have my exam tomorrow.
 
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  • #2
Amith2006 said:
I need help. It’s urgent!
# Assume that in the 70 million electron volt (MeV) betatron, the radius of the stable electron orbit is 28 cm. Calculate the frequency of the applied electric field.
I have found the angular velocity of the electron (w) = 1.07 x 10^9
I assumed that the frequency of the electron= frequency of applied electric field
From that I found the frequency(f) of the
w = 2(pi)f
f = 1.7 x 10^8 Hz
But the answer given in my book is 1.7 x 10^6 Hz. Is it a typographic error?
You have to take into account the relativistic speed here. What did you determine the [itex]\gamma[/itex] to be?

AM
 

FAQ: What Causes Frequency Discrepancies in Particle Accelerator Calculations?

What is a particle accelerator?

A particle accelerator is a scientific instrument that uses electric fields to accelerate charged particles, such as protons or electrons, to very high speeds and energies. These accelerated particles are then used to study the fundamental building blocks of matter and the forces that govern their interactions.

How do particle accelerators work?

Particle accelerators work by using electromagnetic fields to accelerate charged particles in a controlled and precise manner. These fields are created by powerful magnets and radio frequency cavities, which guide and accelerate the particles along a defined path. The particles are then collided or directed into a target, producing new particles and allowing scientists to study their properties.

What are the benefits of particle accelerators?

Particle accelerators have numerous benefits in the fields of physics, medicine, and technology. They allow scientists to study the fundamental building blocks of matter and the laws of nature, leading to advancements in our understanding of the universe. They also have practical applications in medical imaging and cancer treatment, as well as in the development of new materials and technologies.

What are some common problems with particle accelerators?

Some common problems with particle accelerators include technical malfunctions, such as power outages or equipment failures, which can interrupt experiments and cause delays. Other challenges include maintaining the stability and precision of the particle beams, as well as ensuring the safety of the researchers and the surrounding environment.

How are scientists addressing the challenges of particle accelerators?

Scientists are continuously working to improve the design and technology of particle accelerators to address the challenges they face. This includes developing more efficient and powerful acceleration methods, as well as implementing safety measures and protocols. Collaborative efforts and international partnerships also help to advance the field and overcome challenges in particle accelerator research.

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