Cyclotron and Cyclotron Frequency
Summary
TLDRThe script explores the cyclotron, an early high-energy particle accelerator developed by Ernest O. Lawrence in 1930. It describes how the cyclotron uses electric and magnetic fields to accelerate protons to high velocities and energies. The device's structure, consisting of two vacuum chambers and an alternating electric field, is explained. The protons move in a circular path due to the magnetic field and gain velocity through the electric field, eventually exiting to collide with a target, such as a tumor in medical applications. The script also delves into the cyclotron frequency equation, relating it to the particle's motion and the magnetic field's influence.
Takeaways
- 🔬 The cyclotron is an early high-energy particle accelerator developed by Ernest O. Lawrence in 1930.
- 🧲 It uses electric and magnetic fields to accelerate particles, typically protons, to high velocities and energies.
- 🏥 Modern cyclotrons are still used in medicine, particularly for treating tumors with accelerated particles.
- 🛠️ The cyclotron consists of two vacuum chambers and a magnetic field that directs particles in a circular path.
- 🔋 An electric potential difference is created between the chambers to accelerate the particles as they move between them.
- ⚛️ The magnetic field creates a force that causes the charged particles to undergo centripetal acceleration, maintaining a circular motion.
- 🔄 As the particle's velocity increases, so does the radius of its circular path, allowing it to eventually exit the cyclotron.
- 🎯 The exiting particle can be directed towards a target, such as a tumor, for medical treatment.
- 🔀 An alternating electric current is used to create an alternating electric field, which is necessary for continuous particle acceleration.
- 🔁 The frequency of the alternating voltage source must match the cyclotron frequency, which is the frequency of the particle's circular motion.
- ⚖️ The cyclotron frequency can be calculated using the equation derived from the relationship between charge, magnetic field, and mass of the particle.
- 📚 Newton's second law and the right-hand rule are applied to understand the forces acting on the particles within the cyclotron.
Q & A
What is a cyclotron and who developed it?
-A cyclotron is an early high-energy particle accelerator developed by Ernest O. Lawrence in 1930. It uses electric and magnetic fields to accelerate particles, typically protons, to very high velocities and energies.
What is the primary use of cyclotrons in modern times?
-In modern times, cyclotrons are primarily used in medicine for treating tumors by accelerating particles to high energies to target and destroy cancer cells.
What are the two main components of a cyclotron's structure?
-The two main components of a cyclotron's structure are the vacuum chambers and the semicircular vacuum chambers, which create a magnetic field for the particles to move in a circular path.
How does the magnetic field in a cyclotron affect the charged particles?
-The magnetic field in a cyclotron creates a magnetic force that acts as centripetal acceleration, causing the charged particles to move in a circular pathway within the vacuum chambers.
What role does the electric field play in the acceleration of particles in a cyclotron?
-The electric field, created by a voltage difference between the two semicircular vacuum chambers, accelerates the particles linearly when they travel between the chambers, increasing their velocity.
How does the radius of curvature of a particle's path change as it accelerates in a cyclotron?
-As the velocity of the particle increases, the radius of curvature of its circular path also increases, allowing the particle to eventually exit the cyclotron when it reaches a sufficient energy level.
What is the purpose of using an alternating electric current in a cyclotron?
-An alternating electric current is used to create an alternating electric field that changes direction with each half-cycle, ensuring that the electric field always accelerates the particle in the direction of its motion.
What is the significance of the cyclotron frequency in the operation of a cyclotron?
-The cyclotron frequency is the frequency at which the voltage source oscillates, and it must match the frequency of the particle's circular motion to maintain continuous acceleration.
How is the cyclotron frequency related to the particle's motion and magnetic field?
-The cyclotron frequency is determined by the particle's charge, mass, and the strength of the magnetic field. It is the frequency at which the particle completes one full cycle of its circular motion.
What is the equation that describes the magnetic force acting on a charged particle moving in a magnetic field?
-The magnetic force (F) acting on a charged particle with charge (q) moving with velocity (v) in a magnetic field (B) is given by the equation F = q * v * B, where the force is perpendicular to both the velocity and the magnetic field.
How can the period of a particle's circular motion in a cyclotron be calculated?
-The period (t) of a particle's circular motion can be calculated by dividing the circumference of the circle (2 * π * r) by the velocity of the particle (v), which is given by the equation v = q * B * r / m.
Outlines
🔬 Introduction to Cyclotrons and Their Medical Applications
The first paragraph introduces the cyclotron, an early high-energy particle accelerator developed by Ernest O. Lawrence in 1930. It explains how the cyclotron uses electric and magnetic fields to accelerate protons to high velocities and energies. The script describes the cyclotron's structure, including its two vacuum chambers and the magnetic field within them. It also explains the role of the electric field in accelerating particles and how the protons move in a circular path due to the magnetic force. The paragraph concludes with the application of cyclotrons in medicine, specifically for treating tumors by directing accelerated protons towards the tumor.
🔧 The Working Principle of Cyclotrons and Cyclotron Frequency
The second paragraph delves into the working principle of cyclotrons, focusing on the alternating electric field that accelerates the protons. It explains the necessity of an alternating voltage source to maintain the electric field's direction in sync with the proton's motion. The paragraph also introduces the concept of cyclotron frequency, which is the frequency at which the electric field oscillates to keep the protons on their acceleration path. The script provides the equation for the magnetic force acting on a charged particle in a magnetic field and applies Newton's second law of motion to derive the velocity of the particle. It then explains how to calculate the cyclotron frequency using the period of the particle's circular motion and the fundamental constants of the particle's charge, mass, and the magnetic field's strength.
Mindmap
Keywords
💡Cyclotron
💡Particle Acceleration
💡Magnetic Field
💡Electric Field
💡Centripetal Force
💡Velocity Vector
💡Radius of Curvature
💡Alternating Electric Current
💡Cyclotron Frequency
💡Right-Hand Rule
💡Newton's Second Law of Motion
Highlights
The cyclotron was one of the earliest high-energy particle accelerators, developed by Ernest O. Lawrence in 1930.
Cyclotrons use electric and magnetic fields to accelerate particles, usually protons, to high velocities and energies.
Though modern particle accelerators are more complex, cyclotrons are still used in medicine to treat tumors.
The cyclotron consists of two vacuum chambers and a magnetic field that causes charged particles to move in a circular path.
An electric potential difference is created between the two semicircular vacuum chambers to accelerate particles.
The magnetic field provides the centripetal force needed for particles to move in a circular motion within the vacuum chambers.
The electric field in the midsection between the chambers accelerates the particle's velocity as it moves between them.
As the particle's velocity increases, so does the radius of its circular path, allowing it to eventually exit the cyclotron.
The exiting particle can be directed towards a target, such as a tumor, for medical treatment.
The electric field must alternate direction to continue accelerating the particle in the opposite direction after each half cycle.
An alternating voltage source is used to create the alternating electric field needed for continuous particle acceleration.
The frequency of the voltage source must match the cyclotron frequency to synchronize with the particle's circular motion.
The cyclotron frequency is derived from the relationship between the particle's charge, velocity, magnetic field, and mass.
The cyclotron frequency equation is given by f = qb / (2πm), where q is the charge, b is the magnetic field strength, and m is the mass of the particle.
The period of the particle's motion is the time it takes to complete one full cycle in the cyclotron.
The period can be calculated using the circumference of the circular path divided by the particle's velocity.
The cyclotron's practical application in medicine demonstrates the significance of its historical development and ongoing use.
Transcripts
one of the earliest high Energy particle
accelerators was the cyclotron the
cyclotron was developed by Ernest o
Lawrence in 1930 and it basically uses
electric and magnetic Fields to
accelerate particles usually protons to
very high velocities and very high
energies now although modern day high
Energy particles are much more
complicated than the cyclotron the cycle
is still Used in Medicine to treat
tumors so Let's take a look at the
following diagram that basically
describes the structure of our cyclotron
and how it actually works so basically
We have some type of device that creates
a magnetic field so We have two vacuum
chambers vacuum Chamber number one and
semicircular vacuum Chamber number two
now within these vacuum chambers We have
a magnetic field that exists and in this
case the magnetic field points into the
board and That is shown by these Blue
aes with the Circle around them now
between our two semicircular vacuum
chambers We have a Space and within the
Space between these two points We create
An electric potential difference of
voltage difference and this voltage
difference basically creates An electric
field as shown by the these Green arrows
so For This particular Moment or This
particular Moment In Time the electric
field points in this Direction from left
to Right Now That means that this part
has a positive Charge and this part has
a negative Charge now Let's suppose We
take our particle Let's Say A proton and
we place the proton in this location
into Chamber One so We give it some
velocity and When A charged particle in
this case the proton travels inside a
magnetic field What will happen is the
magnetic field will basically create a
magnetic force that will act on our
Charge particle and because the velocity
vector is perpendicular to the magnetic
field the magnetic force will be
perpendicular to both the velocity and
our magnetic field and that means that
magnetic force will act to create
centripetal
acceleration so that magnetic force will
cause the proton To Move in a circular
pathway When that proton is within these
two vacuum chambers so When the proton
is in either one of the two vacuum
chambers the magnitude of velocity does
not actually change However When the
proton travels within this Space Where
We have our electric field there the
velocity will increase because the
electric force as a result of that
electric field will cause that velocity
to increase so When the particle travels
between this midsection its velocity
will increase and when the velocity of a
particle Moving in a Circle increases
the radius of curvature the radius of
that Circle will also inas and so
initially the radius is some small
radius When accelerates the radius
increases and this basically continues
until The radius is large enough And The
velocity is great enough and the Energy
is great enough that the particle
actually exits our cyclotron and when
the particle exits we can play some type
of target object here for example a
tumor and that particle will collide
with that target object so once again a
particle such as a proton begins from
rest It begins To Move in the vacuum
chambers as shown two chambers are
separated by distance as shown in this
diagram and in this Space in this region
here we have an electric potential
difference that creates An electric
field That is used to accelerate that
proton linearly now the magnetic field
inside the two chambers ke the proton
Moving in a circular pathway It doesn't
actually increase the magnitude of the
velocity now as the Speed of the proton
increases its radius of curvature also
increases and eventually as We see in
the diagram the proton leaves the
Chamber and collides with our target so
If We're using this to treat tumor a
tumor We can place a tumor in this
section now notice an important point so
When the proton begins To Move initially
as it exits and begins to travel Through
The Space the electric field has to
Point this way to accelerate the proton
in this Direction in the same Direction
as Motion But when the proton finishes
The Second semicircular loop when it
exits and begins to travel this way we
don't want that electric field to Point
in this Direction because that will
actually stop it instead We want the
electric field to Point In The opposite
Direction and so to create that type of
alternating electric field We use An
alternating electric current so the
voltage source is an alternating voltage
source and it turns out that to keep our
electric field changing every half a
cycle We want the frequency of the
voltage source to be the same as the
frequency of our particle so once again
notice that the voltage source Is
alternating This Is because the electric
field Lines must change directions for
the proton to continue on its
acceleration pathway this implies that
the frequency of oscillation of the
voltage equals to the frequency of the
proton along its circular pathway and
this frequency is known as the cyclotron
frequency So what exactly is the
equation that gives us the cyclotron
frequency well Let's Begin by recalling
What happens inside our two chambers so
whenever We have a positive Charge That
Is Moving with the velocity V inside a
magnetic field B and the magnetic field
is perpendicular to our velocity that
will create a magnetic force on that
object the Charge the magnetic force
will be perpendicular And The magnitude
is given by this equation the magnetic
force acting in the Charge Uh is equal
to the Charge of that particle Q
multiplied by its velocity multiplied by
its magnetic field now to find The
Direction We can apply Right Hand rule
So basically this is our particle our
velocity is going this way the magnetic
field points into the board so that
means We Take The Right Hand We point
this way In The Direction Of The
velocity We curl our fingers into the
board to curl the fingers into our
magnetic field extend the thumb the
thumb points In The Direction of our
magnetic force as shown in this diagram
now Let's Begin by applying Uh newton's
second Law of Motion so the net force
acting on the particle is equal to the
Mass times its acceleration now because
our object isel
a circular fash that means a is equ v s
div r Where v s div r is the centripetal
acceleration the force is given by the
magnetic force
qvb so Let's Take This equation and
solve for the velocity the velocity is
equal to qrb div m notice one of the V
will cancel out now how exactly Can We
find the frequency well rec call That
frequency is related to the period so If
We find the period We can find the
frequency
what So what exactly is the period well
the period is Simply the amount of time
it takes our particle to travel One full
cycle so that means to calculate the
period t We take the distance it travels
in one Circle divided by its velocity
the distance is 2 pi r Where r is the
radius of the Circle So this is our
circumference and we Divide that by the
velocity obtained in this in part one so
We have 2 pi r div qrb div by M The m
Will Go On top the RS cancel and see the
period is equal to 2 pi M div Q m by B
now recall that the frequency is equal
to 1 div by the period so frequencies
equ to 1 div t so We plug in this
equation for t We get this so We see
that the cyclotron frequency is equal to
qb div by 2 m m m by Pi
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