Lista eletro - Italo Albuquerque

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<p>Leista da 1.3. Calculate n curves for five values of AD from to 1, and three values of ND from to On a log-log plot of with from 106 to and from 2 to 105 eV, draw lines of constant AD (solid) and (dashed). On this graph, place the following points (n in m -3 KT in eV): 1. Typical fusion reactor: KT = 30,000. 2. Typical fusion experiments: KT = 100 (pinch). 3. Typical ionosphere: KT=0.05. 4. Typical radiofrequency plasma: n= KT=1.5 5. Typical flame: n= KT=0.1. 6. Typical laser plasma; n = KT = 100. 7. Interplanetary space: n= 106, KT=0.01. 1. 2 l da => - - A3 - 69 Te in = 1 20 (1, =8,93 3 3</p><p>1.3 3 2,35.10 / 2 3. = 3 4. d 17 3 9,98.10 6. ( = 2,35.10 -8 3 = 1,72.10</p><p>1.7. Compute AD and ND for the following cases: (a) A glow discharge, with n= KT,=2eV. (b) The earth's ionosphere, with n= = 0.1 eV. (c) A with n= = 800 eV. a question - 4,86.10 3 1 3 b) = 7430 2 -3 12 = 3 = - 5,43.10 c) - 3</p><p>1.8. In laser fusion, the core of a small pellet of DT is compressed to a density of at a temperature of 50,000,000 Estimate the number of particles in a Debye sphere in this plasma. 1 V 3 2 sendo 3 3/2 / 3/2 3 33 7 1033</p><p>1.11. A field-effect transistor (FET) is basically an electron valve that operates on a finite-Debye-length effect. Conduction electrons flow from the source S to the drain D through a semiconducting material when a potential is applied between them. When a negative potential is applied to the insulated gate G, no current can flow through G, but the applied potential leaks into the semiconductor and repels electrons. The channel width is narrowed and the electron flow impeded in proportion to the gate potential. If the thickness of the device is too large, Debye shielding prevents the gate voltage from penetrating far enough. Estimate the maximum thickness of the conduction layer of an n-channel FET if it has doping level (plasma density) of is at room temperature, and is to be no more than 10 Debye lengths thick. (See Fig. P1.11.) D G Fig. P1.11 1 1 Sendo = 69. 69. 300 22 2 8 10 - - 10 m, a maxima - deve ser menor on igual as compriments</p><p>2.2. In the TFTR (Tokamak Fusion Test Reactor) at Princeton, the plasma was heated by injection of 200-keV neutral deuterium atoms, which, after entering the magnetic field, are converted to 200-keV D ions (A = 2) by charge exchange. These ions are confined only if where a = 0.6 m is the minor radius of the toroidal plasma. Compute the maximum Larmor radius in a 5-T field to see if this is satisfied. Dates A=2; l = mVs 2 E 6 in V</p><p>2.7. An unneutralized electron beam has density and radius a= 1 cm and flows along a 2-T magnetic field. If B is in the direction and E is the electrostatic field due to the beam's charge, calculate the magnitude and direction of the E B drift at r = a (See Fig. P2.7). B2 2a Fig. P2.7 for uma de => = => -pnv E. * de VE = E 14 / -</p><p>2.8. Suppose the earth's magnetic field is 3 10 5 T at the equator and falls off as as for a perfect dipole. Let there be an isotropic population of 1-eV protons and 30-keV electrons, each with density n= at r = 5 earth radii in the equatorial plane. (a) Compute the ion and electron VB drift velocities. (b) Does an electron drift eastward or westward? (c) How long does it take an electron to encircle the earth? (d) Compute the ring current density in dr r B 2 1 2 - 1 - -19 2 eB - 11 1 in - B B = 8 m/s 7 VB Eletrons : =</p><p>2.8 b) Paron c) -8 = 1,87x10 A/m</p><p>2.12. A cosmic ray proton is trapped between two moving magnetic mirrors with = 5 and initially has W = 1 keV and at the midplane. Each mirror moves toward the midplane with a velocity = 10 km/s (Fig. 2.10). 000 B1 L km Fig. 2.10 Acceleration of rays 2.4 Nonuniform E Field 35 (a) Using the loss cone formula and the invariance of find the energy to which the proton will be accelerated before it escapes. (b) How long will it take to reach that energy? 1. Treat the mirrors as flat pistons and show that the velocity gained at each bounce is 2vm 2. Compute the number of bounces necessary. 3. Compute the time T it takes to traverse L that many times. Factor-of- two accuracy will suffice. a) 2 2 2 2 =1 2 S 1 2 2 -</p><p>2.12 - : SkeV b) desde que na = Ap 2 Vm 3,1 4 N=1 2 = 15 104</p><p>2.12 b) L=10 13 12 V AL-</p><p>2.17. A 1-keV proton with in a uniform magnetic field B=0.1 T is accel- erated as B is slowly increased to 1 T. It then makes an elastic collision with a heavy particle and changes direction so that The B-field is then slowly decreased back to 0.1 T. What is the proton's energy now? O pode alteror do proton, inicial do 1 V, proton entra no campo ele Mm A raio do Ele uma medida A com particular sl 6 energia de recus a desse mods or energia do</p><p>3.1 Derive the uniform-plasma low-frequency dielectric constant, Eq. (3.28), by reconciling the time derivative of the equation D = = with that of the vacuum Poisson equation (3.1), with the help of equations (3.24) and (2.67). at onde l sendo E or constante P (EE)</p><p>3.4 Show that the expression for on the right-hand side of Eq. (3.69) has the dimensions of a current density. j D - = KI e BL 3.6 An isothermal plasma is confined between the planes x = in a magnetic field B = The density distribution is (a) Derive an expression for the electron diamagnetic drift velocity VDe as a function of (b) Draw a diagram showing the density profile and the direction of on both sides of the midplane if B is out of the paper. (c) Evaluate VDe at x = a/2 if B = 0.2 KT, =2 eV, and a = 4 cm. = 2x n I eB a2 2 C.B</p><p>3.6 b) no 6 or c) = = 1/0,04 V Pe = n = 33,3 V = m/s De</p><p>3.10 In 2013, the Voyager 1 spacecraft left the heliosphere, the region dominated by solar winds, and entered outer space. The plasma frequency jumped from 2.2 to 2.6 kHz. What was the change in plasma density? razao entre on frequencias 2 V2 - V N1 - - - - 4, de de nov do</p>