The wall divides the town – Nogales Arizona/ Nogales Sonora – though most of the population lives on the Mexican side. On one of the slopes on the US side is a shrine. Ranged along a reinforcement joist slanting from the wall’s concrete base are some burnt-out tealights in glass jars. Knotted to the vertical palings above are a length of curled yellow ribbon and, tied in place with the same kind of ribbon, a bunch of dirty plastic daisies turned brittle by the sun. Nogales Sonora, on the other side, is twenty feet below, and I realise that the wall stands on its own embankment – steep on the Mexico side, like a castle dyke. In order to climb the wall from Nogales Sonora you first have to climb the slope. About thirty-eight feet, all told. Through the wall, in Mexico, I can make out a white, windowless building and a sign: despacho juridico, legal office. Stencil-sprayed on the adjoining wall, a young man’s face – a boy’s really, in its chubbiness – repeated over and over, like a crude Warhol, like a picture of a martyr.

José Antonio Elena Rodríguez died in Mexico; the bullets that killed him were fired here in the United States. It happened on an October night in 2012. Border Patrol had been called to a report of men climbing the wall. As the agents converged, the men climbed back over to Nogales Sonora. A crowd gathered on the Mexican side and began throwing rocks, over the fence, at the patrolmen. Among the rock-throwers was José Antonio Elena Rodríguez (this is the official version). José Antonio Elena Rodríguez threw no rocks, he was merely walking past the fence on the way home from basketball (the unofficial version, the version told by Rodríguez’s friends and family and other civilian witnesses on the Mexican side). The Department of Homeland Security has declined to release its video footage of the incident. It would compromise national security. Everyone agrees that José Antonio Elena Rodríguez was sixteen.

On the twenty-foot-high bluff, behind the eighteen-foot-high fence, stood the eight Border Patrol agents. Among them was Lonnie Swartz. At the foot of the bluff was José Antonio Elena Rodríguez, walking home from basketball, or throwing rocks – both, perhaps – throwing rocks over the top of the fence, thirty-eight feet above him. Again there is no question that Lonnie Swartz approached the fence, and drew his pistol, and shot down on José Antonio Elena Rodríguez, hitting him ten times from behind, pausing only to reload.

The federal investigation rested not only on whether Swartz’s actions were reasonable – he feared for his life, went the defence, rocks big as pomegranates raining down – but whether the killing could even be described as criminal when the kid was a Mexican in Mexico, and therefore exempt from the protections of the US Constitution, and his killer an American in America.

A man stands on an alluvial fan below Tumacacori Mountain, a few dozen miles north of here. His name is José, too: José Salazar Ylarregui. This is 1851. He is a senior member of the Joint United States and Mexican Boundary Commission, responsible for surveying the newly defined southern border. Until 1851 there was no line, no wall. It was war that created the line, the Mexican–American War of 1846, or rather the Treaty of Guadalupe Hidalgo that was the war’s culmination. Salazar, jointly responsible for some hundred men, in the unspeakable heat of the Sonoran Desert, on constant guard against Apaches, made a note. Maybe he imagined his superiors in their cool Mexico City drawing rooms: ‘On paper one easily draws a line with a ruler and pencil.’

In the east, that line followed the natural barrier of the Rio Grande River; in the west it travelled, originally, from El Paso along the Gila River to its confluence with the Colorado, and thence in a straight line to San Diego Bay, placing much of today’s southern Arizona in Mexico. The Gadsden Purchase of 1853 caused the western portion of the line to be repositioned further north. From then on the border, rather than following the course of the Gila, was a straight line from El Paso to the Colorado. Upon a stretch of desert where there were few natural features, and fewer names on the maps of either nation, significance was conjured.

The nature of the border did not escape those tasked with making it a reality. One member of the 1851 survey, observing the newly designated borderlands, asked simply: ‘Is this the land we have purchased, and are to survey and keep at such cost? As far as the eye can reach stretches one unbroken waste, barren, wild, worthless.’ Another described a ‘sterile waste, utterly worthless for any purpose than to constitute a barrier’. Travelling in the region in 1909, the Norwegian explorer Carl Sofus Lumholtz wrote that ‘the sensation was that of walking between great fires’. Until the twentieth century the border was little more than notional: a line on paper echoed by a string of obelisks on the ground, each one separated from its neighbours by two miles of desert; further where conditions were harshest. The statesman’s desert, from the Chinese Taklamakan to the Libyan Sahara: a bulwark, a buffer. But more than that, a weapon for turning your enemies to dust.

Since the 1990s a doctrine known as ‘prevention through deterrence’ has been practised by Border Patrol. Even today, only 351 miles of the 1,954-mile border are effectively fenced – 18 per cent. Increasingly, Border Patrol is deploying remote electronic surveillance technology, the so-called ‘virtual wall’ – infrared cameras, motion-sensors, radar, drones, blimps – but in many places you can still pass from the southern side to the northern with a single step, even if that step must be flanked by a hundred thousand others. Eight kilometres east of Nogales, where the Santa Cruz River crosses (or is crossed by) the border, the fence simply stops, and all one need do in order to move from one country to another is edge along the river’s bank.

The militarisation of the borderlands was accelerated following the terrorist attacks of 2001 and the creation of the Department of Homeland Security. By obliging those who are determined to cross illegally in the harshest areas – the Organ Pipe Cactus National Monument west of Nogales, say – the strategy became one whose efficiency can be measured not only by the number of would-be migrants discouraged from embarking (which is anybody’s guess), but by the number of human remains recovered from arroyos and the shadows of ironwood trees. Between October 2000 and September 2014, in southern Arizona alone, this number was 2,721. Among these people – who succumbed to heatstroke or dehydration, or fell from cliffs or died of snakebite or heart attacks – some eight hundred are unidentified. To this number may be added those remains that have not been found, either because of their remoteness or, more likely, because they have simply been erased.

Like most deserts, the Sonoran is walled in by mountains: to the north and east are the Colorado Plateau, the Rockies and the Sierra Madre; to the west the Sierra Nevada. It is the Sierra Nevada that is responsible for much of south-west America’s aridity, removing the moisture from the Pacific’s clouds as they are drawn up its western flank. They call it a rain shadow, but the effect is not so much a shadowing as a milking. It is from the low-lying south – the tropical south of central America – that the monsoon comes, and the result is a desert that, while being dry enough to kill dozens of people each year, can feel deceptively abundant.

Sometimes the desert preserves – 2,000-year-old mummies have been found under the sands of the Taklamakan, their tongues still pink – but more often, it obliterates. Those shapes helixing high above, shuddering on their huge wings, are turkey vultures, and with the coyotes and the foxes they will strip a body of meat and disperse its bones over a square mile in the course of a few days. As you wait on the Mexican side of the border before trying to enter the desert, therefore, you do so in the knowledge that it is not just your life that you are staking, but – in the absence of your corpse or, if your corpse is recovered, any way of identifying it – your loved ones’ opportunity to grieve for you.

After 9/11, the Department of Homeland Security evolved a new method of ‘deterrence’. It was called ‘enforcement with consequences’. Until then, those apprehended in the desert were processed and dispatched to the nearest port of entry without prolonged detention. This was called ‘voluntary departure’, because the migrant waived his or her right to a judicial hearing. Naturally, once removed from the country, they attempted to cross again as soon as possible – the next day, why not, since they’d come this far. ‘They know the game,’ said a patrolman interviewed at the time. ‘They’re delayed eight hours and then they do it over again.’

Part of ‘enforcement with consequences’, since 2005, is Operation Streamline. It is here that the element of deterrence comes in. Instead of being allowed to leave the US under the terms of ‘voluntary departure’, apprehended migrants are instead processed through the federal criminal justice system. Under Operation Streamline, first-time offenders can be sentenced to up to six months in jail, repeat offenders up to two years.

The city of Tucson lies some sixty miles from the Mexico border, and is often the first objective of undocumented migrants trying to cross the Sonoran Desert. It is also where those who are picked up by Border Patrol are taken for trial. Given the vast numbers of people – tens of thousands – apprehended each year, it is not possible for due process to be applied. This is the nature of streamlining, and it is visible if you go to Tucson’s federal courthouse on any weekday afternoon.

‘Please rise,’ says the judge.

A massed jangling as sixty young men get to their feet. They are manacled and fettered. It is an old, old sound, this jangling, not new to the USA or anywhere else. It is nauseating.

‘When your name is called, please rise and say, present.’ They are tired, and slow. They have come, most of them, directly from a cell, having been picked up in the desert in the past twenty-four hours. Who knows how far they have walked or how long it is since they slept? They look around. The courtroom is cool, high-ceilinged and bright, its walls lined with pastel-coloured fabric. How strange to find yourself here: those days trudging over the hills and arroyos, your clothes shredded by cacti, the birds circling overhead; and then to be transported first to a cell and then to this hushed theatre with its air of privilege, itself symbolic of what you have been seeking, and your appointed attorney placing his bejewelled hand on your shoulder.

‘Jesus Manuel García,’ reads the judge.

‘Presente.’

They are called up to stand before the bench in groups of five or six, the same formulation repeated again and again.

‘Mr Manuel García, did you enter the United States illegally near the town of Nogales on or about 15 September 2015?’

This one has the build of a fourteen-year-old; he is smirking shyly as he lifts himself to his feet. The earphones through which proceedings are being interpreted for him are not working. His attorney intervenes. The attorney is a big, bearded man, and, like his colleagues and the Border Patrol representatives, spends most of the hearing fingering his iPhone.

There is a delay while replacement headphones are found.

‘Gentlemen,’ says the judge, ‘if you don’t understand, please stand, or speak privately to your attorney.’ Nobody stands or approaches his attorney. These are young men, self-conscious among their peers.

‘Mr Manuel García, did you enter the United States illegally near the town of Nogales on or about 15 September 2015?’

There is a pause as Jesus Manuel García listens to the translation.

‘Sí.’

‘You have been charged with illegal re-entry after deportation. Do you understand the charges and the maximum penalties that you are facing?’

A pause.

‘Sí.’ He glances at the men alongside him.

He is wearing a thin hooded jersey in a camouflage pattern, the kind worn by many of his fellow defendants, bought from the stalls catering to migrants on the Mexican side of the border. This is also where you buy your black plastic three-litre canteens and your electrolyte powder and the plimsolls soled with carpet that leave no prints.

‘Mr Manuel García, you have agreed to plead guilty to the petty offence of illegal re-entry. In exchange, the government agrees to dismiss the more serious felony offence against you. Do you understand?’

‘Sí.’

‘Mr Manuel García, please speak up.’

There is a pause, he says it loudly this time, almost shouts. There is laughter among the other defendants.

‘Thank you, Mr Manuel García.’

She asks him how he pleads.

He listens, and says quietly: ‘Culpable.’

‘Thank you, Mr Manuel García. You are going to be deported and removed from the United States. The charge will always be on your record.’

Others, repeat offenders, are sentenced to time in jail – nine months, a year. And yet there is little palpable tension in the room. When Manuel García’s group of half a dozen have received their sentences, they are led from the room. One of them wears a T-shirt with the words keep calm and chive on. I don’t understand what it means. One of them is wearing a white facemask. One of them is on crutches. ‘Bring ’em down!’ comes a warehouse holler.

And so it goes, ‘Culpable’, ‘Culpable’, ‘Culpable’, ‘Culpable’ . . . until, after an hour, the process achieves such momentum that it seems unstoppable, and indeed once those sixty have been processed, another sixty shuffle in, and tomorrow the same, and the next day; and there is nothing in the fashion of the proceedings to give one hope it will ever ease, this filing of people. They jingle as they move, and they move slowly, not only because they are tired, their feet blistered, but because they are shackled. They are sunburned, their arms covered in scratches. They are beyond acknowledging their degradation. After one more round I sidle out into Arizona’s blinding afternoon.

On the other side of the city, in the car park of Southside Presbyterian Church, fifteen men are waiting, Mexicans and Salvadoreans and Guatemalans and Hondurans. They have come here illegally; many have been deported several times. Not all of them are young. On church property they cannot be apprehended by the police or Border Patrol. Citizens of Tucson needing day labour can come here and liaise with the manager, Ereberto, who will allocate the appropriate worker or workers for a set daily fee. For six days a week the men are able to earn a living, at a fair wage and with minimal risk of arrest and deportation. (This is the perennial anxiety – that at any moment, day or night, you might be snatched and shackled and tried and sent back – not to death, necessarily, but to poverty, to chancelessness; to whatever it was that you expended so much energy, so much money, in getting away from.)

I sit among a group of them on the kerb, in the shade of the church wall. We share cigarettes and the cans of San Pellegrino lemonade I’ve brought. Occasionally a truck or car pulls in and one or two of the men are called away by Ereberto to go with the driver to mow a lawn or tile a roof or lay paving or clear a dead person’s house. After an hour, only one guy is left, and in the absence of the others he becomes talkative. His name is Enrique. He is in his early twenties, and wears a young man’s clothes – oversized baseball jersey and jeans, backwards baseball cap over his frizzy ponytail. He lives in the future, when things will be better. After all, his life today is better than it was a year ago, isn’t it? He is quickened by his own words.

It is approaching 2 p.m. and the light has an astringency to it, a penetrating quality that differs from heat. The lemonade is gone, the cans lined up on the kerb between us. He is from Honduras, he says. Like thousands of others each year he crossed Mexico on the roof of La Bestia – the Beast – El tren de la muerte, the notoriously perilous network of freight trains. It took him twenty days to reach Monterrey in the north-east. He had already been deported from that city three times, he says. ‘A lot of people die, you know. You can see a lot of crows beside the tracks. Sometimes on the train people are asking for water or food or money. Bad people. You don’t have money, they push you off the train. I see that kind of people.’

He and two friends from Honduras caught a lift to Sonoyta on the border, and it was from there that they entered the Organ Pipe Cactus National Monument. ‘No fence,’ Enrique says. ‘Only desert. Only desert.’ It took him nine days to reach Tucson. ‘For three days, no water, no food.’ He became separated from his friends when he left them to search for water. ‘I almost died. I was looking for them everywhere. I was screaming, asking names. And I never found them.’

He repeats himself: ‘I spent three days in the desert, by myself.’ He can scarcely believe it. He’s not one of those wide-eyed Salvadorean farm boys with no concept of the desert’s hardships, the sort who enters the desert wearing flip-flops and carrying a few cans of Coke. He had heard the stories, and there he was in the middle of one.

He found a rancher’s water tank. ‘I couldn’t believe that. How God is.’ Then he came upon a can of beans. A can of beans, sitting there in a dry wash! ‘God is the only one. The only one. The beans were bad, but anyway I ate them. They give me energy for two more days. I got lost but then I find a town, I don’t remember the name. A truck driver had a flat tyre. I helped him, and he gave me a ride to Yuma.’

From there he hopped a train to Tucson, hiding in the toilet to avoid the guard. The friends he lost in the desert? They too survived. They are in Indiana, working as roofers. He’s saving for a bus ticket to join them. A car pulls in, and Ereberto is calling him, but he doesn’t stand up. ‘I’m feeling like I am in the middle of my road,’ he says. ‘God is the only one. The only one. The one who choose. If God wants me to go back, I’ll go back.’

The thing about Border Patrol is the solitude. Once you’re trained you’re on your own – stationary in your truck, watching the line for eight, nine hours at a time. You need to know how to take that, John says, as we drive south from Tucson into the desert the next day. He has been well briefed; he is compassionate and reasonable. Nobody wants anyone to die out there. Billy Connolly, he says, was recently a guest. Took him and his crew up in a chopper to film the wall from above. That’s a funny guy.

John himself was once a patrolman, quite senior, but he no longer spends much time in the field, and he misses it. Handholding the media and chaperoning pasty British writers is not real work, to his mind; isn’t the kind of work his father would have admired.

The PR front drops an inch when we stop for a burger at a Wendy’s on the Nogales road.

‘If I was in their shoes? Maybe I’d want to cross, too; but I’ll say this: I wouldn’t cross in the desert; I wouldn’t cross where it’s impossible to carry enough water to keep me alive. I’d cross in one of the towns. Sure, you’re more likely to be apprehended, but you’re a heck of a lot less likely to die.’

His father? A strict man who required academic excellence of his only child. John, no scholar, was punished for his poor grades with long periods locked in his room. He did not become, therefore, a sociable boy, and grew up to experience solitude as if it were normal. It is what made him effective, before he was singled out by his employers for his manner, his diplomacy. It’s a kind of strength, isn’t it, being able to abide solitude?

Following Iraq and Afghanistan and Border Patrol’s corresponding expansion, more and more ex-soldiers have joined up, John says. But BP is not the military; it’s a very particular thing; there’s nothing ‘kinetic’ about it (the army word: kinesis). The job, in essence, is to sit, to watch – and only then, sometimes, to track and to apprehend. You are a security guard (you are also an agent of punishment). To be alone, furthermore, is to be unwitnessed. It is the perennial test of the desert – a challenge to your moral core: when you can do whatever you wish, without anyone there to censure you, apart from those whom you apprehend, how do you behave?

Take a man who has seen action in one desert and put him in another, on his own. A man who’s shot at nameless foreigners and seen those same foreigners shoot back. The way blood can stand on sand for minutes before it sinks in. Put him on the line.

Even in this relatively lush desert there is only so much to occupy the gaze – limestone outcrops, prickly pear, paloverde, mesquite; the sky and its carnivorous birds – before that gaze turns inwards. In the patient desert once again you will find the familiar silence, save for the radio crackle and the wheeling hawks. It is those men who either crack up, says John, or, alert to the danger within themselves, quit.

Coming back from Nogales I’d passed through the checkpoint at Amado on I-19, a dozen agents halting vehicles under a hangar-like white canopy that bridged the northbound road, a secondary line against those who had crossed the border twenty miles south. It’s the scrubby badlands flanking the checkpoint that John and I search, though I’m aware it’s mainly a performance for my benefit. In his green uniform he strides ahead through the gauntlet of ocotillo and cholla as if he is following a scent, blindly; he hardly hesitates. He is at ease here, and he wants to demonstrate that ease. I’m left ten feet back, hurrying to follow him up and down the bouldered arroyos. I’m soon breathless, and pause for water, my feet already blistering in their boots. The up-down terrain unsoftened by vegetation; the dazzle of the sky as you lift your gaze uphill; the heat massing in you.

For John, the trek is not, as it is for me, a mere succession of obstacles. He barely needs to attend to its physical demands; he knows an ankle-turning rock when he sees one, how to negotiate a steep scree slope (crabwise). His focus is the mark that betrays a human’s recent presence; the aberration: broken or pushed-down grass, overturned stones, the slightest darkening of the sparse soil where it has been kicked. It is unforthcoming ground, this shattered limestone; even our own prints are impossible to trace when we turn back.

This is the work, then, the daily work. The country scarcely changes. A week might pass without your apprehending anyone. But that, John says, is not a week of failure. There are, he assures me, no quotas. Sure, a beautiful place to work. But frankly you don’t think much about its beauty.

The ground is littered with discarded belongings. People have been coming this way for years, for generations, in fact. It is one of the great Sonoran routes, following the course of the Santa Cruz River that once, before its water was pumped and diverted from this stretch, snaked between the Santa Rita Mountains to the east and Tumacacori Mountain to the west. I spot a Fruity Shine lip balm and a pair of chrome-plated nail clippers. As if their owners believed they were going somewhere else entirely – a weekend break, a visit to auntie. The artefacts lie there under the ironwood tree where people rested for shade, along with empty water bottles and plastic bags and clothes. All of it slowly being drawn into the rocky ground. It is hard not to be reminded of the aftermath of a great flight; or a rush burial. I look at John with his sidearm in its holster; and, reflected in his Ray-Bans, myself in my sun hat and my rip-proof desert wear. Our breathing is audible.

Back in the truck, we roll slowly along a track, John leaning from his window as he drives, scanning the verge for prints, kick-marks, flattened vegetation. Cutting sign, they call it. This way you scarcely need to leave your vehicle, if you know the roads well enough: just note where the trail crosses the track, and drive to the next road along to see if the trail reappears there. If not, wait; they will come to you, too tired to run.

They have been here, of course, the young men in their many dozens, but not recently. High above us on a knoll, enclosed within a gleaming cyclone fence, stands one of the new line of watchtowers, designed by an Israeli defence firm. We walk to the fence and I look up at it. Its gaze is fixed southwards: radar, high-res video. It is alert to the slightest lateral movement, and in Nogales officers are stationed at their screens, ready to send agents.

In 2014, José Antonio Elena Rodríguez’s mother, frustrated by the slowness of the federal investigation into his killing, sued Lonnie Swartz in federal court. It will come as a surprise when he is indicted for second-degree murder a few weeks from now (he will plead not guilty). I haven’t mentioned the case but John wants to talk about it. He seems tired of toeing the PR line. A rock, if you think about it, he says, delivered with velocity and precision, is a lethal weapon. Ask the Israeli Defence Force. ‘People think, “Hey, that jerk shot him for throwing a little stone.” ’ Next to the track stands a lollipop sign warning of rough conditions ahead. ‘I don’t know what happened, but I know what a rock can do’ – and he crouches, selects a fist-sized chunk of volcanic rock, stands and pulls back his arm and with all his strength launches it at the sign. It hits it in the centre, with an explosion of dust and a report that echoes from the hills.