Physics of Electric Propulsion

Robert G. Jahn

• Publisher: Dover Publications
• Year: 2012
• Print ISBN:
  9780486450407
• eBook ISBN:
  9780486138671
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Geared toward advanced undergraduates and graduate students, this text systematically develops the concepts of electrical acceleration of gases for propulsion. Author Robert G. Jahn, Professor of Aerospace Sciences at Princeton University, starts his presentation with primary physical principles and concludes with realistic space thruster designs.
Part I consists of a survey of those aspects of electricity, magnetism, and ionized gas mechanics that underlie the physical mechanisms for gas acceleration. These topics constitute the main body of the text. Part II's broad division into the categories of electrothermal, electrostatic, and electromagnetic acceleration mechanisms conforms to the historical development of the field and offers conceptual organization for new students.

part one

Physical Background

1

The Province of Electric Propulsion

1-1 HIGH IMPULSE SPACE MISSIONS

The primary attraction of electric thrusters for the propulsion of spacecraft lies in their highly efficient utilization of propellant mass. The corresponding reduction in the propellant supply which must be contained and transported in the spacecraft permits the inclusion of a greater portion of useful payload and the achievement of space missions inaccessible to conventional chemical rockets. Rigorous demonstration of these potentialities involves detailed analyses of specific missions, but the essential concept may be illustrated by basic dynamical arguments.

The flight of a simple rocket in a gravitational field is described by the vector differential equation of motion [1],²

(1-1)

where

acceleration vector of rocket

ṁ = rate of change of rocket mass by exhaust of propellant (a negative quantity)

u_e = exhaust velocity relative to rocket

F_g = local gravitational force

The first term on the right is commonly identified as the thrust of the rocket,

(1-2)

and its integral over a complete mission is called the total impulse,

(1-3)

For a mission of large total impulse requirement, it is apparent that the desired thrust should be achieved via high exhaust velocity rather than by excessive ejection of propellant mass, lest the craft be committed to an intolerably large initial propellant mass fraction. As a simple example, if the rocket operates at constant u_e in a region where the local gravitational field is negligible in comparison with the thrust, or if it exhausts its propellant over a negligibly short interval of time (impulsive thrust), the equation of motion integrates directly to the scalar form

(1-4)

where Δv is the magnitude of velocity increment achieved by the ejection of Δm of the initial mass m₀. By expending all its propellant mass in this way, the rocket can attain a maximum velocity increment

(1-5)

where m_f includes the mass of the rocket casing, engine, tankage, etc., plus useful payload. Conversely, the fraction of the original rocket mass which can be accelerated through a given velocity increment Δv is a negative exponential in the ratio of that increment to the exhaust speed:

(1-6)

Clearly, it is necessary to provide u_e comparable with Δv if a significant fraction of the original mass is to be brought to the final velocity.

More complicated missions of practical interest, involving flight through planetary, lunar, or solar gravitational fields, with variable magnitude and direction thrust programs, staging, etc., can also be represented by characteristic velocity increments Δν, each of which satisfies relation (1-6) for the particular mission involved [2]. In general, long-range missions, such as interplanetary flights, or long-time missions, such as the maintenance of satellite position and orientation for several years, are characterized by correspondingly large Δv. For example, detailed analyses of certain interplanetary missions yield the characteristic velocity increments shown in Table 1-1.

Table 1-1 Characteristic velocity increments for planetary transfer missions

Mission	Δυ, m/sec
Escape from earth surface (impulsive)	1.12 × 10^4
Escape from 300-mile orbit (impulsive)	3.15 × 10^3
Escape from 300-mile orbit (gentle spiral)	7.59 × 10^3
Earth orbit to Mars orbit and return †	1.4 × 10^4
Earth surface to Mars surface and return †	3.4 × 10^4
Earth orbit to Venus orbit and return †	1.6 × 10^4
Earth orbit to Mercury orbit and return †	3.1 × 10^4
Earth orbit to Jupiter orbit and return †	6.4 × 10^4
Earth orbit to Saturn orbit and return †	1.1 × 10^5
† Values are quoted for typical impulsive missions over minimum propellant semiellipse trajectories.

1-2 EXHAUST VELOCITY AND SPECIFIC IMPULSE

The propellant exhaust velocity u_e, which ideally should be comparable with the mission Δv, is determined by the detailed nature of the acceleration of the propellant gas within the rocket. It is directly related to another characteristic parameter of the rocket engine, the specific impulse, defined to be the ratio of thrust to the rate o...

Table of contents

• DOVER BOOKS ON PHYSICS
• Title Page
• Copyright Page
• Dedication
• Preface
• Table of Contents
• List of Symbols
• part one - Physical Background
• part two - Electrical Acceleration of Gases
• Appendix - Space Power Supplies and Low Thrust Mission Analysis
• INDEX
• A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS