50 kilometer Deimos tether  minimum length to remain aloft.
MarsDeimos L1 and L2 are about 14 kilometers from Deimos' surface. Another 26.5 kilometer length extended past these points would balance. Extending the tether 50 kilometers either way along with a counterweight would provide enough tension for the elevators to stay aloft.
Safety
Factor

Zylon
Taper
Ratio

Tether to
Payload
Mass Ratio

1

1.000003

.000007

2

1.000006

.000015

3

1.000009

.000022

Even with a safety factor of three, needed Zylon mass is tiny. Less than a quarter kilogram of tether could handle a 10 tonne payload.
Benefits
There is no net acceleration at L1 and L2, so docking at ports at these locations would be like docking with the I.S.S.
This first step could serve as a scaffolding additional tether infrastructure could be added onto.
2942 kilometer lower Deimos tether
 ZRVTO to Phobos tether
Given an ~1000 upper Phobos tether and a ~3000 lower Deimos tether, it is possible to move payloads between the two moons with almost no reaction mass. The tether points connected by the ellipse match the transfer ellipse's velocities. See my Upper Phobos Tether post.
Safety
Factor

Zylon
Taper
Ratio

Tether to
Payload
Mass Ratio

1

1.01

.04

2

1.03

.06

3

1.04

.09

So even with a safety factor of 3, the elevator's Zylon mass is modest. 1 tonne of Zylon can handle 11 tonnes of payload.
The red transfer orbit pictured above is called a ZRVTO  Zero Relative Velocity Transfer Orbit. At either end of the transfer orbit, relative velocity with the tether at rendezvous point is zero. ZRVTO is a term coined by Marshall Eubanks.
The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication Tethers In Space Handbook. I believe Penzo came up with this idea in 1984.
Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.
Benefits
The idea of ion driven interplanetary vehicles excites me. The Dawn probe has demonstrated ion rockets are long lived and amenable to reuse. An ion rocket's fantastic ISP means a lot more mass fraction can be devoted to the dry mass structure and payload.
However ion rockets have pathetic thrust. They suck at climbing in and out of planetary gravity wells.
Here Mark Adler talks about ion rocket trajectories:
The fictitious Hermes from Andy Weir's The Martian can do 2 mm/sec^{2} acceleration. That would take an implausibly high alpha, But perhaps possible so I will go with that number.
At Deimos' distance from Mars, gravitational acceleration is about 80 mm/s^2. The Hermes' acceleration over Mars gravitational acceleration at that orbit is about 1/40. A small fraction but a lot larger than the 10^3 fraction Adler mentions.
Deimos moves about 1.35 km/s about Mars. With an impulsive chemical burn, it would take about .56 km/s to achieve escape. But with a 2 mm/s^2 acceleration, it would take about 5 days and and .8 km/s to achieve escape.
To spiral down to low Mars Orbit, it'd take Hermes more than 17 days and 3 km/s. So the Deimos rendezvous saves about two weeks and more than 2 km/s delta V.
Once in heliocentric orbit, it is the sun's gravitational acceleration that we put in the denominator. Here is a chart of gravitational acceleration at various distances from the sun:
If the rocket's acceleration is a significant fraction of central body's acceleration, we can model burns as impulsive. The trajectory would be more like an ellipse than a spiral. At earth's distance from the sun., Hermes 2 mm/s^2 acceleration would be about a third the sun's gravity. At Mars, it's about four fifths. In the asteroid belt, Hermes acceleration exceeds acceleration from sun's gravity.
Ion rockets may not be great for climbing in and out of planetary gravity wells. But they're fine for changing heliocentric orbits, especially in the asteroid belt and beyond.
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