Plasma Physics

rockets

AJW August 22, 1997

Rockets
Contents
Basics
Chemical Rocket
Thrust
Specific Impulse
Rocket equation
Efficiency
Trajectories
High-exhaust-velocity, low-thrust trajectories
Plasma and electric propulsion
Fusion propulsion

Basics
A rocket engine is an engine that produces a force, (a thrust) by
creating a high velocity output without using any of the
constituents of the "atmosphere" in which the rocket is
operating. The thrust is produced because the exhaust from the
rocket has a high velocity and therefore a high momentum. The
rocket engine must, therefore, have exerted a force on exhaust
material and an equal and opposite force, the thrust, is, therefore,
exerted on the rocket.
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The fact that the rocket engine does not use any constituent of
the surrounding atmosphere means that it can operate in any part
of the atmosphere and outside the atmosphere which makes it
ideal for space propulsion. There are two basic types of rocket
engine: Chemical Rockets and Non-chemical Rockets .
In a chemical rocket, a fuel and an oxidizer are usually supplied
to the combustion chamber of the rocket. The chemical reaction
between the fuel and the oxidizer produces a high pressure and
temperature in the combustion chamber and the gaseous
products of combustion can be expanded down to the ambient
pressure, which is much lower than the combustion chamber
pressure, giving a high velocity gaseous efflux from the rocket
engine.

Chemical Rocket
There are two types of chemical rockets, Liquid Propellant
Rockets and Solid Propellant Rockets. In a liquid propellant
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rocket, the fuel and the oxidizer are stored in the rocket in liquid
form and pumped into the combustion chamber.

Basic Arrangement of Liquid Propellant Rocket

In a solid propellant rocket, the fuel and the oxidizer are in solid
form and they are usually mixed together to form the propellant.
This propellant is carried within the combustion chamber. The
arrangement of a solid propellant rocket is shown.

Basic Arrangement of a Solid Propellant Rocket.

In a non-chemical rocket, the high efflux velocity from the

rocket is generated without any chemical reaction taking place.
For example, a gas could be heated to a high pressure and
temperature by passing it through a nuclear reactor and it could
then be expanded through a nozzle to give a high efflux velocity.
The term rocket has frequently been used to describe both the
thrust producing device, i.e. the engine, and the whole rocket
powered vehicle. To avoid confusion, especially in the case of
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large vehicles such as space launch vehicles, the propulsion

device is now usually referred to as a rocket engine.
The advantages of liquid-fueled rockets are that they provide
1. Higher exhaust velocity (specific impulse),
2. Controllable thrust (throttle capability),
3. Restart capability, and
4. Termination control.
The advantages of solid-fueled rockets are that they give
1. Reliability (fewer moving parts),
2. Higher mass fractions (higher density implies lower tankage),
3. Operational simplicity.

Liquid propellants
Fuel

Oxidizer

Hydrogen(LH2)

Oxygen (LOX)

450

Kerosene

LOX

260

Monomethyl hydrazine

Isp (s)

(MMH)Nitrogen tetroxide (N2O4) 310

Solid propellants

Fuel

Oxidizer

Powdered Al

Ammonium perchlorate

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Isp (s)
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Year

Event

300 BC

Gunpowder-filled bamboo tubes used

for fireworks in China

1045

Military rockets in use in China

1895

Konstantin Tsiolkovsky derives the

fundamental rocket equation

1926

Robert Goddard launches first liquidfueled rocket

1942

Wernher von Braun's team launches

first successful A4 (V2)

1957

Sputnik launch

1958

Explorer I launch

1967

Saturn V first launch

1969

Apollo 11 Moon launch

Engine design

Chemical-rocket engines combine knowledge of physics,

chemistry, materials, heat transfer, and many other fields in a
complicated, integrated system. The F-1 engine used in the first
stage of the Saturn V rockets that launched the Apollo missions
appears.

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Issues:

Heat transfer (Radiative cooling: radiating heat to space or

conducting it to the atmosphere. Regenerative cooling: running
cold propellant through the engine before exhausting it.
Boundary-layer cooling: aiming some cool propellant at the
combustion chamber walls. Transpiration cooling: diffusing
coolant through porous walls).
Nozzles (Rocket nozzles are usually of an expansion-deflection
design. This allows better handling of the transition from
subsonic flow within the combustion chamber to supersonic
flow as the propellant expands out the end of the nozzle and
produces thrust. Many nozzle variations exist. The governing
equation for the magnitude of the thrust, in its simplest form, is
F = vex dm/dt + (pex - pa) Aex = veq dm/dt, where vex is the
exhaust velocity, dm/dt is the propellant mass flow rate, pex is
the pressure of the exhaust gases, pa is the pressure of the
atmosphere, Aex is the area of the nozzle at the exit, and veq is
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the equivalent exhaust velocity (that is, corrected for the

pressure terms). If the pressure inside the chamber is too low,
the flow will stagnate, while too high a pressure will give a
turbulent exhaust--resulting in power wasted to transverse flow.
Saturn V

Wernher von Braun's team at Marshall Space Flight Center

developed the three-stage Saturn V rocket, shown at right. The
Saturn V served as the workhorse of the Apollo Moon launches.
Its first stage developed over 30 MN (7.5 million lbs) of thrust
and burned about 14 tonnes of propellant per second for 2.5
minutes.

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Space Shuttle

See NASA's Space Shuttle home page.

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Space Shuttle Parameters

Total length 56 m
Total height 23 m
Wingspan 24 m
Mass at liftoff 2x106 kg
Orbiter dry mass 79,000--82,000 kg
Solid-rocket booster thrust, each of 2 15,000,000 N
SSME (main engine), each of 3 1,750,000 N

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Thrust

Consider a control volume surrounding a rocket engine as shown

The net force, F, exerted on the control volume must be equal to

the rate of increase of momentum through the control volume.
But no momentum enters the control volume so Net force on
control volume = Rate at which momentum leaves control
volume
1)

where

2)

is rate at which mass leaves the control volume which, as

indicated in eq. (2), is equal to the rate at which the mass of

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propellant,
, is decreasing with time.
velocity from the nozzle.

is the discharge

The force, , on the control volume arises due to the pressure

force exerted on the gases within the rocket engine and due to
the difference in pressure over the surface of the control volume.
Now, the pressure is the same everywhere on the surface of the
control volume except on the nozzle exit plane which has area
. Hence the net force on the control volume is given by:
3)

But the thrust is equal in magnitude to the force acting on the

rocket,
, so the magnitude of the thrust is given by eqs (1)
and (3) as:
4)

This can be written as follows by using eq. (2):

5)

the negative sign arises because

propellant mass

is decreasing.

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The last term in eqs. (3), (4) and (5) arises because of the
difference between the pressure on the exhaust plane of the
nozzle and the local ambient pressure. As discussed later in this
section, the nozzle is usually designed so that
under a
chosen set of conditions which are usually termed the "design
conditions". In most cases, the pressure term in the above
equations is much smaller than the momentum term and can,
therefore, often be neglected. In this case, the rocket thrust is
given by:

6)

Specific Impulse

Another term that is widely used in defining the performance of

a rocket engines is the Specific Impulse, I. This can either be
defined as the thrust per unit mass flow rate of propellant i.e. as

7a)

or it can be defined as the thrust per unit weight flow of

propellant i.e. as:

7b)

The specific impulse is mainly dependent on the type of

propellant used. An important parameter used in defining the

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overall performance of a propellant is the Total Impulse,

,
which is equal to integral of thrust over the time of operation of
the engine, t, i.e.

8)

If the thrust is constant, the total impulse is given by:

9)

where

is the initial mass of propellant.

Example. A rocket with a mass of 1000 kg is placed vertically

on the launching ramp. If the rate at which the propellants are
consumed is equal to 2 kg/s, find the rocket exhaust velocity
required if the rocket just begins to rise.

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If the rocket just begins to rise, the thrust must be essentially

equal to the weight i.e.

i.e. using eq. (6):

But

= -2 kg/s, M = 1000 kg and g = 9.8 m/s2:

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The required exhaust velocity is, therefore, 4900 m/s. As will be

seen later, this is within the range that is typical of chemical
rockets.
Note: Isp = I / (mp g) = vex / g, where mp is the propellant mass
and g is Earth's surface gravity. In English units, Isp is thus
measured in seconds and is a force per weight flow. Often today,
however, specific impulse is measured in the SI units
meters/second [m/s], recognizing that force per mass flow is
more logically satisfying. The specific impulse is then simply
equal to the exhaust velocity, Isp = vex.
Rocket Equation

In defining the performance of a rocket, the so-called Rocket

Equation is used. This is derived by noting the if M is the mass
of the rocket vehicle at any instant of time and V is its velocity
at this time (see Fig. 6).

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Fig. 6
Force acting on rocket = mass of rocket x acceleration of rocket,
so that if the rocket is moving in a vertical direction:

10)

Hence using eq. (5):

11)

But

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where
is the mass of the vehicle and motor structure and
payload, i.e. the dry mass, which does not change with time and
is the fuel mass, it follows that:

12)

Hence, eq. (11) can be written as:

13)

If the exhaust velocity can be assumed constant, this equation

can be integrated to give:

4)

where

and

are the initial and final masses of the

rocket vehicle and

and
are its initial and final velocities.
Carrying out the integrations then gives:

15)

Defining:
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16)

equation (14) shows that:

17)

In the above analysis, it was assumed that g could be treated as

constant. This may not always be a justifiable assumption.
If the vehicle initially has a velocity of zero, the velocity
achieved when all the fuel has been used, this velocity being
termed the burn-out velocity,

, is given by eq. (17) as:

18)

i.e.

19

being the initial mass of fuel and

structure and the payload,

being the mass of the

being equal to

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propellant has been used at time t. Equation (18) is basically

what is referred to as the rocket equation. The quantity

is the rocket mass ratio.

A high exhaust velocity has historically been a driving force for
rocket design: payload fractions depend strongly upon the
exhaust velocity, as shown (Eqn 17).

It should be realized that in deriving the equations given above

for the rocket velocity, the effects of atmospheric drag have been
neglected. If this is accounted for, eq. (17), for example, will
become:

where D is the drag force acting on the rocket at any instant of

time. Its value depends on the size and shape of the vehicle, the

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velocity, the Mach number and the local properties of the

atmosphere through which the vehicle is passing.
Example. A rocket engine which has an exhaust velocity of
3500 m/s is used accelerate a vertically launched rocket vehicle
to a speed of 4000 m/s. Find the approximate ratio of the
propellant mass to the dry vehicle mass required.
Equation (19) gives:

If it is assumed that gt<<, this equation gives approximately:

i.e.:

Hence,

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Therefore, the fuel mass is approximately twice the dry weight

of the vehicle.
Efficiency

When the total kinetic energy of the rocket and its exhaust are
taken into consideration, the highest efficiency occurs when the
exhaust velocity is equal to the instantaneous rocket velocity, as
shown in figure.

Trajectories

Spacecraft today essentially all travel by being given an impulse

that places them on a trajectory in which they coast from one
point to another, perhaps with other impulses or gravity assists
along the way. The gravity fields of the Sun and planets govern
such trajectories. Rockets launched through atmospheres face
additional complications, such as air friction and winds. Most of
the present discussion treats this type of trajectory.
Advanced propulsion systems and efficient travel throughout the
Solar System will be required for human exploration, settlement,
and accessing space resources. Rather than coasting, advanced
systems will thrust for most of a trip, with higher exhaust
velocities but lower thrust levels. These more complicated
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trajectories require advanced techniques for finding optimum

solutions.
Newton's laws of motion

The fundamental laws of mechanical motion were first

formulated by Sir Isaac Newton (1643-1727), and were
published in his Philosophia Naturalis Principia Mathematica.
They are:
1. Every body continues in its state of rest or of uniform motion
in a straight line except insofar as it is compelled to change that
state by an external impressed force.
2. The rate of change of momentum of the body is proportional
to the impressed force and takes place in the direction in which
the force acts.
3. To every action there is an equal and opposite reaction. (dp /
dt = F)
Calculus, invented independently by Newton and Gottfried
Leibniz (1646-1716), plus Newton's laws of motion are the
mathematical tools needed to understand rocket motion.

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Newton's law of gravitation

To calculate the trajectories for planets, satellites, and space

probes, the additional relation required is Newton's law of
gravitation:
Every particle of matter attracts every other particle of matter
with a force directly proportional to the product of the masses
and inversely proportional to the square of the distance between
them.
Symbolically, the force is F = -G m1 m2 er / r2, where G = 6.67
x 10-11 m3 s-2 kg-1, m1 and m2 are the interacting masses (kg), r
is the distance between them (m), and er is a unit vector pointing
between them.
Kepler's laws of planetary motion

The discovery of the laws of planetary motion owed a great deal

to Tycho Brahe's (1546-1601) observations, from which
Johannes Kepler (1571-1630) concluded that the planets move
in elliptical orbits around the Sun. First, however, Kepler spent
many years trying to fit the orbits of the five then-known planets
into a framework based on the five regular platonic solids. The
laws are:
1. The planets move in ellipses with the sun at one focus.
2. Areas swept out by the radius vector from the sun to a planet
in equal times are equal.
3. The square of the period of revolution is proportional to the
cube of the semi-major axis. That is, T2 = const x a3

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Conic sections

In a central-force gravitational potential, bodies will follow

conic sections.

e is eccentricity and a is the semi-major axis.

Special cases (E is the (constant) energy of a body on its
trajectory).

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Some important equations of orbital dynamics

Circular velocity

Escape velocity

Energy of a vehicle following a conic section, where a is the

semi-major axis

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Lagrange points

The Lagrange (sometimes called Libration) points are positions

of equilibrium for a body in a two-body system. The points L1,
L2, and L3 lie on a straight line through the other two bodies
and are points of unstable equilibrium. That is, a small
perturbation will cause the third body to drift away. The L4 and
L5 points are at the third vertex of an equilateral triangle formed
with the other two bodies; they are points of stable equilibrium.
The approximate positions for the Earth-Moon or Sun-Earth
Lagrange points are shown below.

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Hohmann minimum-energy trajectory

The minimum-energy transfer between circular orbits is an

elliptical trajectory called the Hohmann trajectory. It is shown
for the Earth-Mars case, where the minimum total delta-v
expended is 5.6 km/s. The values of the energy per unit mass on
the circular orbit and Hohmann trajectory are shown, along with
the velocities at perihelion(closest to Sun) and aphelion (farthest
from Sun) on the Hohmann trajectory and the circular velocity
in Earth or Mars orbit. The differences between these velocities
are the required delta-v values in the rocket equation.
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Gravity assist

Gravity assists enable or facilitate many missions. A spacecraft

arrives within the sphere of influence of a body with a so-called
hyperbolic excess velocity equal to the vector sum of its
incoming velocity and the planet's velocity. In the planet's frame
of reference, the direction of the spacecraft's velocity changes,
but not its magnitude. In the spacecraft's frame of reference, the
net result of this trade-off of momentum is a small change in the
planet's velocity and a very large delta-v for the spacecraft.
Starting from an Earth-Jupiter Hohmann trajectory and
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performing a Jupiter flyby at one Jovian radius, as shown, the

hyperbolic excess velocity vh is approximately 5.6 km/s and the
angular change in direction is about 160o.

High-exhaust-velocity, low-thrust trajectories

The simplest high-exhaust-velocity analysis splits rocket masses

into three categories:
1. Power plant and thruster system mass, Mw.
2. Payload mass, Ml. (Note that this includes all structure and
other rocket mass that would be treated separately in a more
sophisticated definition.)
3. Propellant mass, Mp.
Mission power-on time tau
Total mass M0 = Mw+Ml+Mp
Empty mass Me = Mw+Ml
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Specific power [kW/kg]

Propellant flow rate

Thrust power

Thrust

High-exhaust-velocity rocket equation

Assume constant exhaust velocity, vex, which greatly simplifies

the analysis. The empty (final) mass in the Tsiolkovsky rocket
equation now becomes Mw+Ml, so

where u measures the energy expended in a manner analogous to

delta-v. After some messy but straightforward algebra, we get
the high-exhaust-velocity rocket equation:

Note that a chemical rocket effectively has Mw = 0 ==> alpha =

infinity, and the Tsiolkovsky equation ensues. The quantity
alpha*tau is the energy produced by the power and thrust system
during a mission with power-on time

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tau divided by the mass of the propulsion system. It is called the

specific energy of the power and thrust system.
Relating the specific energy to a velocity through E = mv2/2
gives the definition of a very important quantity, the
characteristic velocity:
.

The payload fraction for a high-exhaust-velocity rocket becomes

which is plotted below.

Analyzing a trajectory using the characteristic velocity method

requires an initial guess for tau plus some iterations. The
minimum energy expended will always be more than the
Hohmann-trajectory energy. The payload capacity of a fixedvelocity rocket vanishes at u = 0.81 vch, where vex = 0.5 vch.
Substituting these values into the rocket equation gives

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Example: 9 month Earth-Mars trajectory

(alpha = 0.1 kW/kg, alpha tau = 2x109 J/kg.) NB: When the
distance traveled is factored into the analysis, only u > 10
values turn out to be realistic.

Trade-off between payload fraction and trip time for selected

missions.

Variable exhaust velocity and gravity

Variable exhaust velocity and gravity considerably complicate

the problem. When the exhaust velocity is varied during the
flight, variational principles are needed to calculate the optimum
v(t). The key result is that it is
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necessary to minimize . Even the simplest problem with gravity,

the central-force problem, is difficult and requires advanced
techniques, such as Lagrangian dynamics and Lagrange
multipliers. In general, trajectories must be found numerically,
and finding the optimum in complex situations is an art.

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Plasma and electric propulsion

Year

People

Event

1906

Robert H. Goddard

Brief notebook entry on

possibility of electric
propulsion

1929

Hermann Oberth

Wege zur Raumschiffahrt

chapter devoted to electric
propulsion

1950

Forbes and Lawden

First papers on low-thrust

trajectories

1952

Lyman Spitzer, Jr.

Important ion-engine plasma

physics papers

1953

E. Saenger

Zur Theorie der Photonrakete

published

1954

Ernst Stuhlinger

Important analysis. I
ntroduces specific power

1958

Rocketdyne Corp.

First ion-engine model

operates

1960

NASA Lewis; JPL

NASA establishes an electric

propulsion research program

1964

Russians

Operate first plasma thruster

in space (Zond-2)

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Plasma physics overview

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Key equations Maxwell's equations for the microscopic electric

(E) and magnetic (B) fields

Electrostatic potential definition and Poisson's equation

Lorentz force on a particle of charge q

The result of this equation is that charged particles spiral along

lines of magnetic force with the gyrofrequency (cyclotron
frequency)

at a distance called the gyro radius (Larmor radius)

,
where

is the average thermal velocity of a particle.

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Because the electron's mass is much smaller than any ion's mass,
the electron gyrofrequency is much faster than the ion
gyrofrequency and the electron gyro radius is much smaller.
The Lorentz force leads to several charged-particle drifts, even
in static electric and magnetic fields. These are:
ExB drift:

Grad-B drift:

Curvature drift:

Plasmas Will Try to Reach Thermodynamic Equilibrium.

Neglecting boundary effects, equilibrium is represented by the
Maxwell--Boltzmann or Maxwellian distribution of particles in
energy,

where n0 is the average charge density and Boltzmann's constant

is kB = 1.38 x 10-23 J/K = 1.6 x 10-19 J/eV. The latter value is
given because it is often convenient to measure plasma energies
and temperatures in electron volts, eV, rather than Kelvin, K (1
eV = 11,604 K).

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Plasmas are Dynamic Entities

Electrons are extremely mobile. For example, the typical

velocities for ions and electrons in a hydrogen plasma are

Debye Shielding

An important consequence of the high plasma mobility is Debye

shielding, in which electrons tend to cluster around negative
density fluctuations and to avoid positive density fluctuations.
The Debye length, or Debye screening distance, gives an
estimate of the extent of the influence of a charge fluctuation. It
plays an extremely important role in many problems. The
Debye length is given by

Plasma Parameter

The number of particles, N, in a Debye sphere (sphere with

radius equal to the Debye length) must satisfy N>>1 in order for
there to be statistical significance to the Debye shielding
mechanism:

In general, the condition N>>1 is necessary for collective effects

to be important.

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Electrostatic potential sheaths

Near any surface, and sometimes in free space, electron and ion
flows can set up electrostatic potential differences, called
sheaths. Commonly, these are approximately three times the
electron temperature. Physically, sheaths set up in order to
conserve mass, momentum, and energy in the particle flows.
Sheaths repel electrons, which have high mobility, and attract
ions. Free-space sheaths are called double layers.
Quantum mechanics and atomic physics

Quantum mechanics enters the world of plasma thrusters

because line radiation--the light emitted when electrons move
down energy levels in an atom--can be a significant energy loss
mechanism for a plasma.
Other important phenomena include collisions and charge
exchange (electron transfer between ions and atoms or other
ions). Two important plasma regimes for radiation transport can
be analyzed with relative ease:
Local thermodynamic equilibrium (LTE)
High density plasma, so collisional effects dominate
radiative ones.
Characterized by the electron temperature, because electrons
dominate the collisional processes.
Coronal equilibrium
Optically thin plasma
Collisional ionization, charge exchange, and radiative
recombination dominate.

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High-Exhaust-Velocity Thrusters

Plasma and electric thrusters generally give a higher exhaust

velocity but lower thrust than chemical rockets. They can be
classified roughly into five groups, the first three of which are
relevant to the present topic and will be discussed in turn.
Electrothermal
Resistojet
Arcjet
RF-heated
Electrostatic
Ion
Electrodynamic
Magnetoplasmadynamic (MPD)
Hall-effect
Pulsed-plasma
Helicon
Photon
Solar sail
Laser
Advanced
Fusion
Gas-core fission
Matter-antimatter annihilation
Tether
Magnetic sail

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Electrothermal thrusters

This class of thrusters (resistojet, arcjet, RF-heated thruster)

does not achieve particularly high exhaust velocities. The
resistojet essentially uses a filament to heat a propellant gas (not
plasma), while the arcjet passes propellant through a current arc.
In both cases material characteristics limit performance to values
similar to chemical rocket values. The RF-heated thruster uses
radio-frequency waves to heat a plasma in a chamber and
potentially could reach somewhat higher exhaust velocities.
Electrostatic thrusters (ion thrusters)

This class has a single member, the ion thruster. Its key principle
is that a voltage difference between two conductors sets up an
electrostatic potential difference that can accelerate ions to
produce thrust. The ions must, of course, be neutralized--often
by electrons emitted from a hot filament. The three main stages
of an ion-thruster design are ion production, acceleration, and
neutralization. They are illustrated in the figure below. The basic
geometry of an actual ion thruster appears at right on the cover
from a recent Mechanical Engineering (from PEPL home page).

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Fission reactors are located at the ends of the long booms in

these nuclear-electric propulsion (NEP) systems. These and
other designs are shown on NASA Lewis Research Center's
Advanced Space Analysis Office's (ASAO) project Web page.
NEP Mars approach

Hydra multiple-reactor NEP vehicle

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Electrodynamic thrusters
Magnetoplasmadynamic (MPD) thruster

In MPD thrusters, a current along a conducting bar creates an

azimuthal magnetic field that interacts with the current of an arc
that runs from the point of the bar to a conducting wall. The
resulting Lorentz force has two components:
Pumping: a radially inward force that constricts the flow.
Blowing: a force along the axis that produces the directed
thrust.
The basic geometry is shown from a computer simulation done
by Princeton University's Electric Propulsion and Plasma
Dynamics Lab. Erosion at the point of contact between the
current and the electrodes generally is a critical issue for MPD
thruster design.

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Hall-effect thruster

In Hall-effect thrusters, perpendicular electric and magnetic

fields lead to an ExB drift. For a suitably chosen magnetic field
magnitude and chamber dimensions, the ion gyro radius is so
large that ions hit the wall while electrons are contained. The
resulting current, interacting with the magnetic field, leads to a
JxB Lorentz force, which causes a plasma flow and produces
thrust. The Russian SPT thruster is presently the most common
example of a Hall-effect thruster.

Pulsed-plasma thruster

In a pulsed-plasma accelerator, a circuit is completed through an

arc whose interaction with the magnetic field of the rest of the
circuit causes a JxB force that moves the arc along a conductor.

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Helicon thruster

The principle of the helicon thruster is similar to the pulsedplasma thruster: a traveling electromagnetic wave interacts with
a current sheet to maintain a high JxB force on a plasma moving
along an axis. This circumvents the pulsed-plasma thruster's
problem of the force falling off as the current loop gets larger.
The traveling wave can be created in a variety of ways, and a
helical coil is often used. The plasma and coil of a helicon
device is shown.

Useful references on plasma and electric thrusters

Robert G. Jahn, Physics of Electric Propulsion (McGraw-Hill,
New York, 1968).
Ernst Stuhlinger, Ion Propulsion for Space Flight (McGraw-Hill,
New York, 1964).
Fusion propulsion

1950's to 1970's: Conceptual designs were formulated for both

D-3He and D-T fusion reactors for space propulsion. These
included simple mirror reactors and Toroidal reactors with
magnetic divertors. Both type-II superconductivity and fusion
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power were new concepts in the early 1960's when the first D3He design was performed. Three recent advances enhance the
feasibility of D-3He reactors for space applications.
Lunar 3He resources
More credible physics concepts
Advances in technology
Two interesting early papers on D-3He space-propulsion reactors
are Englert (1962) and Hilton, et al. (1964). These papers
followed much of the same logic given in the present discussion
to propose using the D-3He fuel cycle in linear magnetic fusion
reactors. Although we now know that the simple-mirror concept
used in the earliest papers cannot achieve a sufficiently high Q
(ratio of fusion power out to required input power), which
probably must be on the order of 10 or more, they presented
many interesting ideas and recognized several important
engineering approaches.
Later papers, such as Roth, et al. (1972), examined the idea of
adding 'bucking' coils to extract a magnetic flux tube from a
toroidal magnetic fusion reactor and exhaust the thrust.
Although this geometry may work in relatively low magnetic
field toroidal reactors, it would require massive coils and be
extremely difficult for the present mainline concept, the tokamak
(see lecture 26), where the magnetic fields in conceptual designs
approach practical limits of about 20 T.

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Magnetic fusion fuels for space applications

Advantages of D-3He magnetic fusion for space applications

No radioactive materials are present at launch, and only
low-level radioactivity remains after operation.
Conceptual designs project higher specific power values (1-10 kW-thrust per kg) for fusion than for nuclear-electric or
solar-electric propulsion.
Fusion gives high, flexible specific impulses (exhaust
velocities), enabling efficient long-range transportation.
D-3He produces net energy and is available throughout the
Solar System.
D-3He fuel provides an extremely high energy density.

D-3He fuel is more attractive for space applications than D-T

fuel.
High charged-particle fraction allows efficient direct
conversion of fusion power to thrust or electricity.
Increases useful power.
Reduces heat rejection (radiator) mass.
Allows flexible thrust and exhaust velocity tailoring.
Low neutron fraction reduces radiation shielding.
D-3He eliminates the need for a complicated tritiumbreeding blanket and tritium-processing system.

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Shown below are the fusion power density in the plasma and the
fraction of fusion power produced as neutrons for D-T and D3He fuel.
Fusion Power Density

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Neutron Power Fraction

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The high fusion power density in the plasma favors D-T fuel,
but the reduced neutron power fraction favors D-3He fuel. This
trade-off exemplifies the competition between physics and
engineering in fusion energy development. In reality, a balance
among these and other considerations must be found. For space
applications, D-3He fuel has usually been projected to be most
attractive. The key reason for this is that the most important
factor is not the fusion power density in the plasma (kWfusion/plasma volume) but is the engineering power density
(kW-thrust/mass of reactor and radiators). Several factors
contribute to the dominance of D-3He fuel:
Reduced neutron flux helps greatly
Reduced shield thickness and mass
Reduced magnet size and mass
Increased magnetic field in the plasma
Direct conversion can be used to increase the net electric
power if plasma thrusters are needed.
Many configurations can increase magnetic fields (B fields)
in the fusion core, gaining power density from a B4
scaling.

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Regarding the last point, magnetic-fusion configurations can be

classified as in the following table:

B at limit

B near limit

Relatively low B

S/c tokamak

Copper tokamak

Field-reversed
configuration

Stellarator

Heliotron

Spheromak

Torsatron

Tandem mirror
Bumpy torus
Reversed-field pinch

Energy density of space-propulsion fuels

A fundamental limit on the specific power available from a fuel

is the energy density of that fuel. A realistic assessment, of
course, requires the detailed design of fuel storage and a means
of converting fuel energy to thrust. Nevertheless, a high fuel
energy density is desirable, because it facilitates carrying excess
fuel, which contributes to mission flexibility, and indicates the
potential for a high specific power.

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The argument is often forwarded that antimatter-matter

annihilation is the best space-propulsion fuel. A key difficulty
exists, however: antimatter takes much more energy to acquire
than it produces when annihilated with matter. Presently the
ratio is about 104, and there appears little likelihood that ratios
below about 102 are accessible. Antimatter, therefore, will
probably be of limited use for routine access to the Solar
System, although it will be the fuel of choice for specialized
applications, such as interstellar missions. The energy needed to
acquire various fuels is compared with the energy released in
burning them in the figure .

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High efficiency is critical in space

The ratio of useful thrust energy, which scales with efficiency,

to the waste heat, which scales with (1 - efficiency), is a strong
function of the efficiency of converting the fusion power to
thrust. Because radiators often contribute a substantial fraction
of the total rocket mass, efficiency generally is an important
parameter.

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Fusion Reactor Designs for Space Applications

Conceptual designs of magnetic fusion reactors for space

propulsion during the past decade have generally calculated
specific powers of 1-10 kWthrust/kg reactor. The projected
specific powers for selected designs appear in the table below.
Note: Widely varying assumptions and levels of optimism have
gone into these conceptual designs and the resulting specific
powers.
Author

Year

Configuration

Borowski

1987

Spheromak

10.5

Santarius

1988

Tandem Mirror

1.2

Chapman

1989

FRC

Haloulakis

1989

Colliding Spheromaks

Bussard

1990

Riggatron Tokamak

3.9

Bussard

1990

Inertial-Electrostatic

>10

Teller

1991

Dipole

1.0

Carpenter

1992

Tandem Mirror

4.3

Nakashima

1994

FRC

1.0

Kammash

1995

Gas Dynamic Trap

21(D-T)

Kammash

1995

Gas Dynamic Trap

6.4(D3He)

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Various fusion-reactor configurations have been considered for

space applications. Generally, the key features contributing to an
attractive design are
D-3He fuel
Solenoidal magnet geometry (linear reactor geometry) for
the coils producing the vacuum (without plasma) magnetic
field.
Advanced fusion concepts that achieve high values of the
parameter beta (ratio of plasma pressure to magnetic-field
pressure).

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Field-reversed configuration (FRC)

Engineering schematic (DT version)

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Tandem mirror engine

Tandem mirror with life support and other systems

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Spheromak

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Inertial-Electrostatic Confinement (IEC)

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VISTA ICF space-propulsion design

Some Inertial-confinement fusion (ICF) reactors for space

propulsion have also been designed. One example is VISTA,
shown at right. Because of fusion burn dynamics, D-3He fuel is
much harder to use in ICF reactors, and VISTA used the D-T
fuel cycle. The British Interplanetary Society's earlier Daedalus
study used D-3He fuel, but had to simply assume that the
physics would work.

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References on fusion for space propulsion

R. W. Bussard, "Fusion as Electric Propulsion,'' Journal of
Propulsion and Power 6, 567 (1990).
R. W. Bussard and L. W. Jameson, "The QED Engine Spectrum:
Fusion-Electric Propulsion for Air-Breathing to Interstellar
Flight,'' Journal of Propulsion and Power 11, 365 (1995).
A. Bond, A. R. Martin, R. A. Buckland, T. J. Grant, A. T.
Lawton, et al., "Project Daedalus,'' J. British Interplanetary
Society 31, (Supplement, 1978).
S. K. Borowski, "A Comparison of Fusion/Antiproton
Propulsion Systems for Interplanetary Travel,''
AIAA/SAE/ASME/ASEE 23rd Joint Propulsion Conference,
paper AIAA-87-1814 (San Diego, California, 29 June--2 July
1987).
S. A. Carpenter and M. E. Deveny, "Mirror Fusion Propulsion
System (MFPS): An Option for the Space Exploration Initiative
(SEI),'' 43rd Congress of the Int. Astronautical Federation, paper
IAF-92-0613 (Washington, DC, 28 August--5 September, 1992).
S. Carpenter, M. Deveny, and N. Schulze, "Applying Design
Principles to Fusion Reactor Configurations for Propulsion in
Space,'' 29th AIAA/SAE/ASME/ASEE Joint Propulsion
Conference, paper AIAA-93-2027.
R. Chapman, G.H. Miley, and W. Kernbichler, "Fusion Space
Propulsion with a Field Reversed Configuration,'' Fusion
Technology 15, 1154 (1989).
G. W. Englert, "Towards Thermonuclear Rocket Propulsion,''
New Scientist 16, #307, 16 (4 Oct 1962).

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