PPPL
QUIZ: INTRODUCTION TO PLASMA PHYSICS
The basic properties of plasmas, the “fourth state of matter”, will be reviewed. This is introductory, elementary text-book material.

(click on a question to show/hide answers)
1. What is a plasma ?
  • 1.  Plasma is derived from the Greek word “φάντασμα”, or “phantasma”, meaning phantom or illusion. This word is used by scientists when describing something vague or uncertain (and when they want to sound intelligent). The fact is, nobody even really knows what exactly a plasma is!

    2.  Plasma, which is a fluid, is the clear, liquid component of blood that remains after red blood cells, white blood cells, platelets and other cellular components are removed. It is the single largest component of human blood, comprising about 55%, and contains water, salts, enzymes, antibodies and other proteins.

    3.  Plasma is the pressurized, colorful “solidified liquid” found in high-quality televisions and other electronic appliances. (Do not puncture the screen, or the solidified liquid will condense to gas and escape, and the television will no longer work.)

    4.  Plasma is an ionized, quasineutral gas, for which a sufficient number of atoms have lost electrons and for which self-generated electric and magnetic fields result in collective behavior.

    5.  None of the above, or some of the above.

    6.  All of the above, or none of the above.

    [#q1]

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      The correct answer is 5
      In the field of medicine, plasma would most commonly refer to that component of blood described in (2), so (2) is correct. When talking physics, plasma is an ionized gas, so (4) is also correct. When a gas is sufficiently hot, the electrons may have sufficient thermal motion so that they can escape the atomic structure, and atoms collide and knock electrons of each other. Charge separation between the resulting ions and electrons give rise to electric fields. Charged-particle flows, i.e. currents, give rise to magnetic fields. In addition to the usual physics phenomena displayed by gasses, in plasmas the electric and magnetic fields result in long-distance, collection motions. Irving Langmuir called this state of matter “plasma”, which is derived from the Greek word “πλάσμα” meaning that which has been moulded or formed. At Princeton Plasma Physics Laboratory (PPPL), we study the physics of ionized gases.
2. Where are plasmas to be found naturally occuring in nature ?
  • 1.  Plasmas are found in fires, thunderstorms, and in “sparks”.

    2.  Plasmas are not really things can be found; rather, they must be created artificially in the laboratory.

    3.  Plasmas are found in the eonosphere between the photophosophere and the exosphere, and are usually called the “Eastern lights” (aurora admodum). They appear similar (but fainter and more colorful) to the better-known “Nothern lights” (auroras borealis).

    [#q20]

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      The correct answer is 1
      A common feature of plasmas is that they glow, i.e. they emit light, when electrons drop back down through the energy levels in the excited atoms and ions. Naturally occuring plasmas include: lightning, the auroras borealis and australis (or the northern and southern lights), lightning, the sun and the stars, the solar wind. (Note that there is no such thing as the “Eastern lights”!) Plasmas are also found in fluorescent and neon lights. In fact, given that the stars are in the plasma state, about 99% of the matter in the known universe is a plasma!
3. How many ionized atoms compared to neutral atoms are to be expected in a gas ?
  • 1.  Singly charged ions combine to create doubly charged ions, so the number of ions is given by the Fibonacci sequence.

    2.  The number of ions compared to neutrals increases with temperature.

    3.  Gases are electrically neutral; therefore, the number of ions is identically zero.

    [#q30]

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      The correct answer is 2
      The Saha equation shows that the amount of ionization, $n_i/n_n$, where $n_i$ and $n_n$ are the number density (per $m^3$) of ionized atoms (which are called “ions”) and neutral atoms (sometimes called “neutrals”), to be expected in a gas in thermal equilibrium is given by \begin{eqnarray} \frac{n_i}{n_n} \approx 2.4 \times 10^{21}\frac{T^{3/2}}{n_i} \exp(-U_i/kT), \end{eqnarray} where $T$ is the gas temperature (in Kelvin, K), $k=1.3804 \times 10^{-23}J/K$ is Boltzmann's constant, and $U_i$ is the characteristic ionization energy of the gas (defined as the amount of energy required to remove an outermost electron from an atom). The degree of ionization is negligible at room temperature for nitrogen gas (which is the primary component of air), but the degree of ionization increases with temperature. This is why plasmas exist in astronomical bodies with temperatures of millions of degrees, but not on earth. (Content extracted from [1].)
      [1] F. Chen, Introduction to Plasma Physics and Controlled Fusion, Plenum Press (1984)
4. What is the “Deflector Shield” ?
  • 1.  The Deflector Shield (DS) describes how ions repel ions and electrons repel electrons. The DS measures the distance of closest approach of two colliding like-charges, and is function of particle velocity and impact angle.

    2.  The Deflector Shield has nothing to do with plasmas. It is the name of a Star Trek shield that “deflects” incoming attacks (from Klingons!).

    3.  The Deflector Shield is used to prevent the plasma from cooling and to protect the external environment from x-ray emission. It is usually a high-Z material used to coat the plasma chamber.

    [#q21]

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      The correct answer is 2
      Not all physicists are “Trekkies”, but we do tend to believe that scientific research can create a technologically advanced society that will raise living standards and protect the environment by, for example, providing clean renewable energy.
5. Which statement is correct regarding the motion of charged particles in magnetic fields ?
  • 1.  The magnetic field exerts a force on charged particles that, in the absence of collisions (i.e. friction), accelerates the particles to relativistic velocities, at which point the relativistic mass provides a counter-balance.

    2.  In a constant and uniform magnetic field, a charged particle trajectory is a helix with its axis parallel (or anti-parallel) to the magnetic field.

    3.  Magnetic fields do not affect the motion of charged particles directly; however, magnetic fields are synonymous with electric fields, which do (obviously) accelerate electrically charged particles, and thereby magnetic fields can indirectly influence particle motion.

    [#q22]

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      The correct answer is 2
      The force exerted by a magnetic field, ${\bf B}$, on a charged particle, with charge $q$ moving with velocity ${\bf v}$ is given by the “Lorentz force”, ${\bf F} = q \, {\bf v}\times{\bf B}$. Note that ${\bf v}$ and ${\bf B}$ are vectors (which means that they have magnitude (i.e. size) and direction), and the vector cross-product gives a force that is perpendicular to both ${\bf v}$ and ${\bf B}$. Forces that are perpendicular to the velocity often result in circular motion: imagine swinging a stone tied on a string - in what direction is the instantaneous velocity of the stone, and in what direction is the instantaneous force exerted on the stone by the string? There is no force in the direction parallel to ${\bf B}$, so the parallel velocity is constant. The vector addition of the perpendicular circular motion and the parallel constant motion results in the charged particle making a helical motion. The radius of the helix is called the “gyro-radius” and is given by $r = m v_\perp / q B$, where $m$ is the particle's mass and $v_\perp$ is the magnitude of the velocity perpendicular to ${\bf B}$.
6. How are plasmas made in the laboratory ?
  • 1.  When a critical level of plasmonic material is compressed, a spontaneous chain reaction will create plasmas.

    2.  Small explosions of plasmons create an energy-cascading avalanche that results in plasmas. This method mimics the lightning process.

    3.  A small amount of gas is heated and ionized by driving an electric current through it, or by shining radio waves into it.

    4.  Plasmas can be made by rubbing two sticks together.

    [#q28]

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      The correct answer is 3, and maybe 4.
      The gas needs to be heated without heating the container surrounding the gas, as otherwise the container would melt! This can be achieved by driving an electric current through the gas, or by shining radio waves into the container, for example. For short plasma pulses, the thermal capacity of the container may be sufficient to accommodate the heating of the container by the plasma, and for longer-pulse operation the container may need to be actively-cooled.
      As for rubbing two sticks together, perhaps if a sufficient amount of heat is created so that the sticks catch fire then, well, yes, fires contain plasmas; but please do not light fires in the laboratory unless a responsible adult is present, or more importantly a fire extinguisher.
      [1] R. J. Goldston & P.H. Rutherford, Introduction to Plasma Physics, IOP Publishing (1995).
7. What is the “phase-space density of particles” ?
  • 1.  It is a function, $f({\bf x},{\bf v})$, that gives the number of particles at a given location, ${\bf x}$, and with a given velocity, ${\bf v}$.

    2.  It is a multi-valued function, ${\bf f}(T)$, that gives the number of atoms to be found in the solid, liquid, gas and plasma state for a given temperature.

    3.  It is a relative measure, ${\cal F}({\cal \Omega})$, of the concentration of particles as they change their physical states. A higher phase-space density measurement, paradoxically, implies a greater inter-particular separation, e.g. water while in its solid state.

    [#q31]

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      The correct answer is 1
      When considering a large number of particles, scattered throughout a region of space, and moving at different speeds in all directions, quantitative calculations often depend on knowing how many particles are where and what their velocities are. The phase-space density, $f$, quantifies the number of particles per unit of $dx\,dy\,dz\,dv_x\,dv_y\,dv_z$, the volume element of six-dimensional phase space. The three-dimensional integral of $f$ over all velocities, ${\bf v}$, gives the number density of particles per unit volume of ordinary physical space, which we denote $n$, \begin{eqnarray} n \equiv \int f \; dv_x\,dv_y\,dv_z. \end{eqnarray} (Extracted from [1].)
      [1] R. J. Goldston & P.H. Rutherford, Introduction to Plasma Physics, IOP Publishing (1995).