Consider a mirror machine in the following Figure, which has the following magnetic field in a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a mirror machine in the following Figure, which has the following magnetic field in a cylindrical coordinate, B(r, 2) = B. (1+)2 - B, ) Plasma B pax Answer the following questions. [30 points] (a) Consider a particle moving along the z-axis (r-0). Evaluate z(t) for the motion of the guiding center if the position and velocity at time t-0 are z(t = 0) = 0 v(t = 0) = vo1f + Voz2 where vo1 and voz are the constants. [10 points] (b) Assume that there are two particles A and B, as described in (a). At z-0, the particle A has vo1 = Vov1/3 and voz = Vov2/3, while the particle B has vo1 = Vov2/3 and voz = Vov1/3. Before approaching to the location of z = 1, are the particle A and B trapped (is there reflecting point)? Assume that the particle is not trapped if its reflecting points are z > L.Find the solution of (b). Show that the motion is sinusoidal, and calculate its frequency. Use the initial conditions as the conditions (z-0 at t=0) in (a). [10 points] (c) What is the magnetic field gradient drift (VB drift) at z = 0 and r = 1/2 ? [10 points] Consider a mirror machine in the following Figure, which has the following magnetic field in a cylindrical coordinate, B(r, 2) = B. (1+)2 - B, ) Plasma B pax Answer the following questions. [30 points] (a) Consider a particle moving along the z-axis (r-0). Evaluate z(t) for the motion of the guiding center if the position and velocity at time t-0 are z(t = 0) = 0 v(t = 0) = vo1f + Voz2 where vo1 and voz are the constants. [10 points] (b) Assume that there are two particles A and B, as described in (a). At z-0, the particle A has vo1 = Vov1/3 and voz = Vov2/3, while the particle B has vo1 = Vov2/3 and voz = Vov1/3. Before approaching to the location of z = 1, are the particle A and B trapped (is there reflecting point)? Assume that the particle is not trapped if its reflecting points are z > L.Find the solution of (b). Show that the motion is sinusoidal, and calculate its frequency. Use the initial conditions as the conditions (z-0 at t=0) in (a). [10 points] (c) What is the magnetic field gradient drift (VB drift) at z = 0 and r = 1/2 ? [10 points]
Expert Answer:
Related Book For
Posted Date:
Students also viewed these electrical engineering questions
-
Which character in the following figure is exclusively shared by taxa C and D? 5. A 1, 3 2.
-
The investment shown in the following figure has an annual equivalent worth of $200 at i = 8%. Determine the cash flows in periods 2, 3, 5 and 6. $400 $400 3 4 5 6. Years $2,145
-
The scatter chart in the following figure was created using sample data for profits and market capitalizations from a sample of firms in the Fortune 500. a. What does this scatter chart indicate...
-
How does the range of hFE (Fig. 3.23j, normalized from hFE = 100) compare with the range of hfe (Fig. 3.23f) for the range of IC from 0.1 to 10 mA?
-
Olga Conrad, a financial writer, noted recently, "There are substantial arguments for including earnings projections in annual reports and the like. The most compelling is that it would give anyone...
-
(c) At resonance, what is the phase angle of the source current with respect to the source voltage? How does this compare to the phase angle for an L-R-C series circuit at resonance? (d) Draw the...
-
Locate an article that discusses an injunction that has been obtained by a party in California. What was the defendant enjoined from doing? Was this a temporary, preliminary, or permanent injunction?...
-
The following are typical questions that might appear on an internal control questionnaire for payroll activities: 1. Is there adequate separation of duties between employees who maintain human...
-
The details of a project are: Equity raised for the project: 60 lakhs Debt taken: 30 lakh Cost of debt (ka): 8% Cost of equity (ke): 18% Calculate the cost of capital for the project.
-
Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in...
-
An option portfolio has a delta of 100 and a vega of 50. (a) If you can use the stock and a delta-neutral straddle with vega of 10 to hedge, how many shares of the _) you need to neutralize the...
-
What is the standard structure of a business memo, and how should each section be formatted to enhance readability and clarity? Discuss the role of headings, bullet points, and white space in memo...
-
On January 1 Primary Manufacturing had a beginning balance in Work-in-Process Inventory of $82,000 and a beginning balance in Finished Goods Inventory of $22,000. During the year, Primary incurred...
-
Len is a keen rugby fan. He sees this advertisement: Rugby World Cup in Australia Be There! See 8 rugby games including one semi-final and the final: Then spend 10 days touring the Australian Outback...
-
#2: If 2 masses 7 kg and 17 kg have velocities <6,-10 > and respectively, find the final velocities of the 17 kg objects a) Find the final velocity of the 5 kg object if the collision is elastic...
-
Evaluate, correct to 2 decimal places When a = 3.43 b=1.55 c = 5.78 d = -0.26 ab-cd c2 d
-
Firm A signed a lease contract with an equipment dealer on January 1, 2022. Firm A needs to make a rental payment of $80,000 at the beginning of each year, with the first payment due immediately. The...
-
Write a program that initializes an array. It inputs a value from the user and searches the number in the array.
-
Diagrammatically represent a Lorenz curve that signifies a Gini coefficient of zero.
-
Monetary policy can be conducted in various ways. 1. Explain why the demand for reserves curve is downward sloping. 2. Explain where the supply of reserves comes from. 3. Explain why the supply of...
-
Refer to the accompanying figure. Because of a cartel agreement, a firm has been assigned a production quota of q2 units. The cartel price is P2. What do the firms profits equal if it adheres to the...
-
The equations of motion of a two-degree-of-freedom system are given by where \(F_{1}(t)\) denotes a rectangular pulse of magnitude 5 acting over \(0 \leq t \leq 2\). Find the solution of the...
-
Find the response of a simple pendulum numerically by solving the linearized equation: \[\ddot{\theta}+\frac{g}{l} \theta=0\] with \(\frac{g}{l}=0.01\) and plot the response, \(\theta(t)\), for \(0...
-
Find the response of a simple pendulum numerically by solving the exact equation: \[\ddot{\theta}+\frac{g}{l} \sin \theta=0\] with \(\frac{g}{l}=0.01\) and plot the response, \(\theta(t)\), for \(0...
Study smarter with the SolutionInn App